Quantitative Mass Spectrometry of Solids E. B. OWENS and N. A. GlARDlNO Lincoln Laboratory, Massachusetts Institute o f Technology, Lexington 73, Mass.
b Some sources of error in mass spectrometry have been investigated. It is concluded that with the proper development, calibration, and photometry procedures and by applying the appropriate corrections for ion mass and energy, photographic detectors can be used in mass spectroscopy with reasonable accuracy. The large errors that are experienced in solids mass spectrometry probably originate in the spark ion source. A number of processes occur simultaneously in the spark source and contribute in unknown proportions to the total error. This source must be studied further before it can be used for quantitative trace analysis.
I
THE early 1930’s collaboration between F. W. Aston and the Ilford Co.’s laboratories resulted in the production of the Ilford Q plates. The Q emulsion is made in three types (13): &I, low speed, small grain, and high contrast; Qz, intermediate in speed, grain size, and contrast; and Q, high speed, large grain, and low contrast. Good results have been achieved using the Q1emulsion for isotope abundance measurements (I@, but the Q2emulsion, because of its greater speed and intermediate granularity, has been the most widely used emulsion for general analytical mass spectrometry. A recent comparison of several emulsions by Rudloff ($1) indicates that Eastman SWR emulsion may be equal to or better than any of the Ilford Q emulsions. The SWR plates combine the high sensitivity a t low exposures of the &, emulsion with the steeper slope of the calibration curve characteristic of the Q1 emulsion. The work reported in the present paper was done entirely with Ilford Q 2 emulsion.
N
PHOTOGRAPHIC DETECTION
Emulsion and Development Uniformity. The uniformity of photographic response over the total surface of a plate depends on both the uniformity of the emulsion applied to the plates and the ability of the experimenter to develop equally all portions of the emulsion. To minimize the photographic development variations, a mechanical developer (18) was built which provides uniform agitation and 1172
ANALYTICAL CHEMISTRY
good temperature control during a carefully timed photoprocessing procedure. With this equipment, the combined effects of emulsion and development variations were shown to be 5% or less. Since this variation results not only from the nonuniformity of the emulsion but also from errors in making replicate exposures, the nonuniformity of the development process, and errors of densitometry, it is felt that the variation in emulsion uniformity is probably smaller than the total variation, although the possibility of compensating errors must be acknowledged. Thus it appears that emulsion nonuniformity makes only a small contribution to the over-all analytical error. It was also shown, however, that the development error is appreciably larger when the hand development technique described by Aston (f?) is used. While the data reported represent the uniformity of only one plate, no significant departure from this example has been experienced in two years of using However, other Ilford Qt plates. workers ($4) have reported much larger variations which they associate with changes in emulsion thickness. This unevenness of thickness was seen by observing a t oblique angles the reflection of the darkroom safety light on the surface of the plate. Clearly, plates with such obvious defects are not suitable for quantitative analyses. The emulsion sensitivity has been found at times to vary aa much as 50% from plate to plate within the same emulsion batch. Data obtained from several plates of the same batch can be corrected for the plate-to-plate variation through the use of standard exposures of an elemental sample put on each plate. As might be expected, the emulsion characteristics vary even more widely between batches of the emulsion than between plates of the same batch. Consequently, large errors will be introduced in both minimum detection limits and concentration ratios unless each batch of plates is calibrated individually. Emulsion Calibration. To calibrate the photographic emulsion one must determine the relationship of film response to film exposure over the exposure range from barely detectable images to film saturation. The data for calibration are usually obtained by putting on a single plate a series of spectra having known relative
exposure values. Such a series is easy to produce if the ion source delivers into the mass spectrograph an ion beam that is constant in time. In this case the required variation in exposure is achieved by varying the exposure duration. The calibration curve obtained by this method is satisfactory if the reciprocity failure of the emulsion is not too large. Lichtblau and Mattauch (15) discuss and give an example of this method of calibration. Unfortunately, the vacuum spark source ion yield is very erratic in time, and the analyst must replace the spark source used for the analysis of solids with a constant ion source if he wishes to use the above method of calibration. A method of calibration which does not depend on either the time constancy of the ion yield or the validity of the reciprocity law for the emulsion has been reported by Mattauch and Ewald (16). This method uses a spectrum of an element which has a large number of isotopes with abundances ranging in reasonably spaced steps from low to high values. Plotting the observed opacities of the isotope lines from a single spectrum against the known abundances gives a calibration curve in relative terms. Some of the elements having enough isotopes in proper abundances to be usable for this method are hafnium, krypton, tellurium, tin, xenon, and zinc. The method is satisfactory, having only the minor fault that in calibrating an emulsion of wide latitude, such as Ilford Q2, it may be difficult to determine the shape of the calibration curve over the entire latitude with only six or seven points. A calibration method has been used in our laboratory which, like the Mattauch-Ewald method, does not depend upon the constancy of the ion source or the validity of the reciprocity law. This method, which is essentially the same as that described by Duke (T), is an adaptation of the two-line technique used for many years by emission spectrographers for optical spectra as described by Churchill (4)and in the ASTM Tentative Standard Practice E 116-59 T (1). The somewhat similar method described by Dornenburg and Hintenberger (6) must be used with caution, since it ignores the possibility that charge exchange collisions add to the intensity of one of the lines used for the calibration. The calibration data for the authors’
r f SaArK LLECTHODES
ENERGY STOP 8 B E A M MONITOR E L E C T R O D E
b
MAGNET,C SECTOR
E L t CTRIC SECTOR
PLATE
I
Figure 1. Simultaneous photographic and electrometric detection
I
\
ELECTROMETER DETECTOR
method are obtained by comparing lines of two isotopes of a given element in a series of spectra ranging in exposure from the lightest to the darkest lines that can be measurec on a microphotometer. It is prefer,ible if the abundance ratio of the two isotopes lies between 1.2 and2.0, because we have found that for such isotopes the line widths measured at one-half peak ion density will be essentially the seme. The abundance ratio of the two isotopes equals the ion density ratio of the two ion beams. This method has the advantage over the Mattauch-Ewald method that one can obtain a large number of points for plotting the calibration curve over the full usable range of the emulsion. In addition, 35 elements have isotopes with abundance ratios in the preferred range, including Si, Cle, Ga, and Sbconstituent elements of prominent semiconductor materials. For this reason the calibration data frequently can be obtained from the graded series of exposures usually made of the sample for analysis. The calibration curves obtained by the two-line and the Mattauch-Ewdd methods show the relationship between relative exposure and relative transmittance (% T). Either method can be made absolute if the absolute number of ions forming one of the lines used can be determined accurately. A method for making this measurement, shown in Figure 1, consists of mounting an electrometer detector on the photographic plate holder in ,suchmanner that the singly charged ions of one isotope of the test element go through the slit of the electrometer detector while, at the same time, the singly charged ions of another isotope hit the plate. Using this system to calibrate in absolute terms, we find that with 15-kv. ions of atomic mass 100, about 1 x 106 ions per sq. mm. are required to make a detectable image on Ilford Qz plates. Corrections for Line Width and Background. The method presented here for line width correction requires measurement of the width of each
1
10.3
95.5
52.5
line. For this reason it does not require either perfect focusing or knowledge of the theoretical line width, as does the method used by Mattauch and coworkers (16, 16). The trace produced by the strip recorder as the photometer scans a spectrum line does not accurately depict the ion distribution in the beam causing that line, since the photometer response produces a % T trace. An ion density trace can be obtained by a point by point replot of the yo T trace in terms of ion densities obtained from the calibration curve. The total number of ions causing the line is represented by the area under this ion density trace. If the ion density trace shows reasonable symmetry, the area can be approximated closely by multiplying the peak ion density value by the width of the trace a t one-half peak ion density. The background correction is made by subtracting the ion density of the background from the peak ion density for the line. If the spectrophotometer trace (% T trace) is reasonably symmetrical, the point by point replot of the % T trace in terms of ion density is not required for the background and line width corrections. These calculations can be made directly from the % T trace as illustrated in Figure 2 and Table I. A straight line ( A , Figure 2) is drawn on the microphotometer trace from the background on one side of the spectral line to the background on the other side. Another line ( B )is drawn through the point of minimum % T on the trace and at right angles to the mass coordinate. The point a t which lines A and B cross indicates the background level of the spectral line.
In Figure 2 and Table I, yo T , is the % T of the line peak, % Ta is the back-
ground of the line, I , is the ion density corresponding to yo T, as determined by the calibration curve, and similarly I b is the ion density corresponding to yo Tb. ZP - I6 or I , gives the peak ion density corrected for background. I J 2 gives the half-peak ion density, and
Table 1.
Data Treatment
0.8
51.7
25.9
Figure 2. Background and line width corrections
+
IJ2 I, gives the half-peak ion density plus background. % T., is the % T value corresponding to an ion density as determined from the of I c / 2 calibration curve. W is the width of the microphotometer trace at the level % T.,-Le., the width a t half-peak ion density. The apparent yield, N = I , X W , is proportional to the total number of ions forming the line. (The term “apparent yield” is used here, since this value must be corrected for the effect of ion energy and mass, as discussed below.)
+
This method was used with all of the data reported in this paper. The validity of this method of line width correction was tested by changing the magnet to photoplate distance between successive exposures, thereby broadening the lines. In each exposure the same number of ions struck the plate. Though the line width varied as much as a factor of 2, the number of ions determined from the photographic data corrected for line width was constant to within 10%. The total method of calibration and background and line width corrections was tested by measuring the isotopic distribution of Pt. The measured values and the currently accepted values are compared in Table 11. The fact that
26.7
18.4
5.9
VOL. 35, NO. 9, AUGUST 1963
305
0
1173
L
1
ION ENERGY, k e v I L L
11- I
375
-
75
IiO
Figure 3. Photogr a p h i c sensitivity vs. ion energy, 3.875 to 15 k.e.v.
isotope ratios can be determined Iyith the good agreement as shown in Table 11, whereas error factors of 2 or 3 are common in determining element ratios, indicates that the major causes of the latter errors are not photographic or photometric processes but parts of the overall analytical procedure. Emulsion Response vs. Ion Energy. In a recent paper ( 1 7 ) , one of the present authors has shown that the sensitivity of Ilford Q2 emulsion increases with increasing ion energy. This effect must be considered when comparing sensitivity limits obtained under different experimental conditions. It is also important in calculating the number of multiply charged ions, since the ion energy is the product of the ion charge and the accelerating potential. As stated in the previous work, the data showing the effect of ion energy had not been corrected for line width. These data have n o v been recalculated, correcting for line width and background and at the same time putting the data in a form which more directly shows the energy effect on quantitative analysis. Briefly, the experimental procedure was to make equal exposures with 3.75-, 7.5-, and 15-kv. accelerating potentials, using singly charged ions from samples of single elements of high
Table II.
Isotope 190 192 194 195 106
198
1174
purity (carbon, silicon, zinc, molybdenum, tin, and platinum). The magnetic field strength was adjusted for each set of exposures so that for a given element the singly charged ions maintained the same radius of curvature through the magnet section regardless of accelerating potential. In this manner, any effect that ion path might have on instrumental transmission was kept constant for ions having the same mass. The plates were developed in the developing equipment described above and the spectrum lines were measured in a recording densitometer. The apparent yield, A; (last column of Table I), was calculated for the lines measured, using the method explained above in which corrections are made for line IT-idth and background. The results are shown in Figure 3. Since the exposures were constant, the varying apparent yield shows the effect of ion energy on photographic response. To estend the studies t o higher ion energies, new data were obtained for ions of 30- and 45-k.e.v. energy by measuring lines due to doubly and triply charged ions accelerated with 15-kv. potential. The system shown in Figure 1 was used t o provide electrometric detection of the fl, +2, or + 3 ions of one isotope of the test element simultaneously with photographic detection of the +1, + 2 , or + 3 ions of another isotope. Data were collected for equal numbers of singly, doubly, and triply charged ions of hfo and Si, the magnetic field strength being varied to maintain a constant path for the ions being measured. These results and the data from the previous experiments at lolver energies, all calculated as apparent yield with corrections for line width and background, are plotted in Figure 4. It is apparent from Figure 4 that the photographic response is approximately proportional to the ion energy in the range of 3.75 to 45 k.e.v. (The data obtained lvith 1.875-kv. accelerating potential, shown in the previous paper are not used here. because the irregular shape of many of the lines obtained with that energy made the present method of line width correction invalid.)
L.
I
ION ENERGY, k e v
5
IO
50
Figure 4. Photographic sensitivity vs. ion energy, 3.875 to 4 5 k.e.v.
Emulsion Response os. Ion Mass. Owens (17) presented a plot showing the effect of the ion mass on the re>pome of Ilford Q2 emulsions. However, the method of line width correction used mas of unknown validity and no correction mas made for the possible difference in instrumental transmission occurring for ion beams traveling different paths through the magnet section. Since the magnet field was held constant. the path length through the magnet section varied with the square root of the ion mass. Thus. for a mass range of 13 t o 198 the path length variation was considerable. To eliminate these shortcomings, nen experiments have been performed in which the magnet strength was varied so that all test ions, regardless of mass, traversed appro\imately the same path. The samples were single elements of high purity and a total beam esposure vas chosen so that 1.2 x 10: singly charged ions of one of the isotopes of cach test elcmcnt would strikc tlic plate. Standard P t exposures were made on each plate to permit corrections for plate-to-plate variations in sensitivity. bll test lines and the standard Pt lines nere measured on the recording densitometer and the apparent yields
Platinum Isotope Distribution
DeterTrue % 0.013 0.78 32.9 33.8 25.3 7.21
mined
%
Av. error
...
0.68 32.4 35.7 23.7 7.55
ANALYTICAL CHEMISTRY
...
0.10 0.6
ION M A S S , ornu
1.9 1.6
0.34
2:
4'0
Figure 5.
60
Bo
, 100
~. I20
14-0
-
.. IS0
Id0
Photographic sensitivity vs. ion mass
I ZO'J
calculated as explained above. Taking the muelsion sensitivit:; to 198Pt+ ions as unity, the relative emulsion sensitivity to any other tast ion was calculated by dividing tht: apparent yield for the test ion by the a 3parent yield for lg3Pt ions. The relative sensitivities are plotted as a function of ion mass in Figure 5. The data are well represented by the function s = \/Mpt/MJ where M p t is the mass of 198Ptand M is the mass of the ion under test. +
SPECTRUM ANALYSIS
The preceding sectior has treated the problem of determining the number of ions detected in a given mass position from measurements of the photographic image produced by tkose ions. The next step is to perform the spectrum analysis from these line measurements. The qualitative problem of determining the exact masses of the ions forming the spectrum lines and the proper element identific.ttion from these mass values are not considered in this paper. The general method of mass calculation is well known and the refinements to obtain more exact mass determinations depend largely on the particular instrument used. Several tables of isotope massf's and of mass spectrum lines (11, 1.6, 19) are available to assist in element identification. It is assumed for the purposes of this paper that the lines being measured have been identified properly and :ire k n o m to be free from interference. In turning to the quantitative aspects of the spectrum analysis it is evident that the total number 0 ' ions of a given element reaching the Flate is not obtained from the measurement of one line. The ions of a given element form many spectrum lines due to isotope distribution, multiple ionization, formation of polyatomic clusters and charge exchange collisions. The determination of the total ion yield of 5 given element requires the measurement and summation of all of these lines, with appropriate corrections for ion majs and energy. The complete spectrum analysis could be accomplished by determining in this manner the total yield for every element appearing in the spectrum. [Calculations of ion yield are difficult for lines which are due to a combination of polyatomic clusters and ions which have experienced chargth exchange collisions. For example, a collision in which the charge on a 69Ga+(or ?lGa+) ion changes from +2 to +1, denoted %+I, will yield a line voincident with the line of the dimer Wa69Ga+ (or 71Ga71Ga+). But no charge exchange collision will cause a line coincident with the mixed dimer, 69Ga71Cla+. Similarly, 3-1 charge exchange collisions will J ield lines coincident w th the trimers 69Ga69Ga69Ga+ and i1Ga71Ga71Ga+but
not coincident with 69Ga69Ga71Ga+or 69Ga71Ga71Ga'. The contribution of the charge exchange collisions to the 69Ga69Ga+lines may be estimated by comparing the intensities of the 69Ga69Ga+ and the 69Gai1Galines and correcting for the relative probabilities of the formation of the two dimers. These probabilities have been discussed and tabulated (29). Though this calculation gives only approximate values, it contributes but a small error to the total yield value, since the number of ions landing at the dimer and trimer positions often is less than 1% of the total yield for the element. J While the concentration of every element in the spectrum can be calculated from the measurement of every line of every element with reasonable rigor, this calculation would obviously be very time-consuming. Consequently, it is usual to calculate the relative concentrations of the element in the spectrum from the measurement of only one line for each element. The yield of monatomic ions of element X having charge j and free from charge exchange collisions can be calculated from one line as outlined in Table I. This yield is related to the total amount of that element in the spectrum as follo~vs:
where
S L I= , number of ions of isotope i of element X with charge jyield measured from one spectral line SP = total number of ions in beam reaching photographic plate -4,, = fractional abundance of isotope i of element X B,, = that fraction of ions of element X which had j electrons removed during ionization C, = concentration of element X in total ion beam reaching photographic plate D,, = that portion of B,j that does not experience charge exchange collision E, = that portion of element X forming polyatomic clusters For any two elements X and Y the concentration ratio in the spectrum is
The yield ratio obtained from the measurement of one line of each element and corrected for isotope abundance will equal the concentration ratio of X to Y in the spectrum only if the two elements have the same charge distribution in the ion beam reaching the plate, the charge exchange processes are of equal proportion for the two elements, and the same fraction of each element forms polyatomic clusters. An examination of
these factors is desirable if one would better understand the analytical difficulties. Charge Distribution. Various estimates have been given for the ion charge distribution occurring in an r.f. vacuum spark. The values given for the ratio of doubly charged to singly charged ions range from 1:3 to 1: 10 (3, 6, 7, 20). Some workers have assumed a constant factor for each degree of ionization and used multiply charged ion lines in an analysis by multiplying the apparent yield by the appropriate factor. However, no data have been published to support any factor or to establish that any factor is constant for all elements in all exposures. The charge distribution has therefore been studied by obtaining spectrograms of various materials with several source conditions. The spark source pulse length and repetition rate were controlled by the settings of the pulse generator supplied with the mass spectrograph, while the sparking voltage was controlled by adjustment of the r.f. oscillator plate voltage on the spark source. However, the effective spark voltage depends on the breakdown potential of the spark gap. It is not known at present how much this breakdown potential varies from the voltage indicated by the control settings. The pulse length and repetition rate of the pulse generator output were measured with an oscilloscope. These measured values are given in Tables 111, IV, V, VI, and VII. To ascertain if the actual spark conformed to the output of the pulse generator, a photocell was positioned a t the window of the source chamber to detect the light emitted by the spark. The output of the photocell was put into an oscilloscope. It was found that the ratio of the number of sparks to the number of r.f. oscillations in a pulse was variable and always less than unity. The sparking began with the first r.f. cycle of each pulse and ended toward the end of the pulse Ehen the last few cycles of the pulse decreased in magnitude. The actual spark pulse length varied between 75 and 99% of the pulse length measured a t the pulse generator output. This variation was not a function of the pulse length, but was controlled by the spark gap geometry and spacing. Since these were constantly changing because of sample consumption, it was difficult to maintain a constant sparking efficiency for more than a few minutes. Thus, the pulse repetition rate measured at the output of the pulse generator is the true repetition rate, but the actual pulse length varies from 75 to 99% of the value reported. The singly, doubly, and triply charged lines were measured on a recording microphotometer and the apparent yield was calculated as explained above. VOL. 35, NO. 9, AUGUST 1963
0
1175
Table 111. Pulee length, Met.
Pulses per sec.
5 5 5 50 40 160
100 1000 1000 1000 100 100
Proportion of +1 Ions
(Ga-48) Spark voltage, Ga+/total kv. Ga, % 30 30 90 30 30 30
Table IV.
+/total
As,%
96 96 85 61 89 89
Proportion of $ 1
%+
Ga total As++-Astot&l
91 90 94 70 85 85
1.06 1.07 0.91 0.87 1.05 1.05
79
1.12
83 75 83 84
1.00 1.06 1.15 1.12
Ions
(GaSb) W C .
per sec.
kv.-
5 5 5 50 40 160
100 1000 1000 1000 100 100
30 30 90 30 30 30
Table V. Pulse length, Mec.
.
89 84
85 79 95 94
Proportion of +1 Ions
(In&) S ark rofiage, In+/total kv. In, %
Puleea per aec.
h + / t o t a l IC As, % As+
total ’
A0
total
5 5 50 100 100
40 160
30 30
Table VI.
95 92
Proportion of + 1
87 73
1.09 1.27
94 94 91
1.02 1.03 1.05 1.05 1.08 1.10
Ions
(InSb)
5 5
5 50 40 160
per 8ec.
kv.-
100 1000 1000 1000
30 30 90 30 -~ 30 30
io0
100
Table VII.
96 96 96 95 94 94
90 ~.
~~
88 86
Proportion of $ 1
Ions
(Stainless steel) Av.
x+ ~-
.-
Fe+
Pulse length, peec. 5 20 15 15
1176
-
Spark
Pulses voltage, per eec. kv. Cu 100 100 100 1000
75 75 75 75
79 76 75 78
ANALYTICAL CHEMISTRY
Ni 78 73 74 72
X+/total x, % Fe hln 81 79 76 78
76 74 71 73
x total
Cr
Ti
Fe total
82 81 79 79
80 78 79 80
0.98 0.96 1.01 0.99
The data were corrected for ion energy, using factors obtained from Figure 4. Neither charge exchange linea nor polymer lines were visible in any of the exposures used. Therefore, they represented well below 1% of the total ion beam. The triply charged ion lines were weak and equal to about 1%or less of the total ion beam. Therefore, the total yield was considered to consist only of singly and doubly charged ions, and the charge distribution was calculated as per cent of singly charged ions of an element in the total yield of that element. The results for the elements in GaAs, GaSb, InAs, InSb, and stainless steel are given in Tables 111, IV, V, VI, and VII, respectively. The uncertainty of the data is about 5%. No consistent relationship is discernible between charge distribution and source conditions. The last column in these tables gives the proportion X+/Y+ c total X/total Y , which shows the relationship between the element-to-element concentration ratios as calculated from the singly charged ion lines alone and the same ratios as calculated from the total yield of those elements. From these data i t is concluded that in these experiments calculation of element concentrations from measure ments of singly charged ion lines alone would not change the results on the average by more than 10% of the yield. However, since the ratio of doubly charged ions to total yield for a given element varies more widely, much greater errors would be incurred if the concentration were determined using only doubly charged ion lines. Charge Exchange Processes. Ions passing through the mass spectrograph occasionally collide with residual gas molecules or free electrons. The collision may result in a gain of an electron by the ion. Ions experiencing such “charge exchange collisions” travel a different path after the collision than they would have if they had not gained the electron. Obviously then, the number of ions of mass A4 and charge c arriving a t the photoplate a t the position appropriate for the specific mass M / c will be reduced by that proportion of those ions which experience charge exchange collisions. The probability of an ion experiencing a collision depends only on the residual gas pressure and the free electron density existing along the ion path. Ions of elements X and Y traveling through the instrument simultaneously see the same gas pressure and electron cloud and therefore have the same collision probability. Although the concentrations of X and Y map be different, the proportion of ions undergoing collisions will be the same for element X as for element Y. However, the probability that a collision will result in a charge
exchange is very like y to depend on the nature of the ion involved. Thus the proportion of ions of any element X that exp1:riences a collision causing the ion charge to change from q1 to qt depends on the fraction of ions initially having charge ql, the probability of such ions having a collision while passing betwetin the electrostatic and the magnetic sections, and the probability of the collision causing a charge exchange. While we have been able to make some evaluation of the first two processeg, the third remains unknown. Fortunately, in most spectra this lack of inforniation contributes little to the over-a,,l error, since the charge exchange lines of an element usually constitute le% than 1% of the total yield for that element. Polyatomic Clusters. The ratio of polyatomic to monatomic ions has been investigated by Franzen and Hintenberger (8). The ratios of diatomic and triatomic ions to monatomic ions as taken from the graphs in their paper for six elements are shown in Table VIII. These i*esults do not take into account the fact that charge exchange collisions may add to the intensity of polyatomic lines. The true proportion of polyatomic ions therefore will be equal to or less t tan the results reported. These data show that for the elements investigated the polyatomic clusters constitute but a negligible portion of the total ion yield. If the total yield of the element being determined is high, the polyatomic lines will appear and can be evalua1;ed. Where such evaluation cannot be made, the resultant error in assessing the concentration of an elerient will probably be small, judging from the data in Table VIII. This cannot be stated with certainty until more data are obtained. From the preceding discussion it is seen that the varioLs sources of error involved in the analysis of a spectrum are unlikely to cortribute the large errors that have been reported in mass spectrographic analysis. But the discussion has considered only the composition of the spectrum or effectively the composition of the ion beam as it arrives at the plane of the photographic plate. The comparison of the known composition of standard samples with the analysis of the spectra obtained from these samples reveals the existence of factors that cause the ion beam and sample compositions to differ. ANALYTICAL RESULTS
Table IX gives t f e results of mass spectrographic analysis of four 111-V 3emiconductor compounds. The values given are the conclwtrations of the group 111 element in the compound and were reproducible to within 10% of the
value. The GaAs 1 sample has been sparked for several hours before the exposures represented here were made. The data for GaAs 2 were from exposures of fresh samples. Obviously, after prolonged sparking Ga and As are not entering the ion beam equally. However, in only a few cases do the other data differ from the expected value of 50% by more than the experimental error.
Table IX. Pulse length, pec. 5
5 5 50 40 160
Pulse8 per sec. 100 1000
1000
1000 100 100
Table VIII. Ratio of Polyatomic to Monatomic Ions (8)
-xz XI X
Element Carbon
Copper Iron
Magnesium
Titanium
Aluniinum
6
XI z
2
x
lo-*
x
10-6
10-4
10-2 1 . 5 x 10-4 10-8 2 X 10-3 3 x 10-1
5
lo-' 10-4 lo-'
Analysis of Ill-V Semiconductor Compounds
Spark voltage, kv. 30 30 90 30 30
30
-
GaAs 1 96 97 78 87 89 87
The known concent,rations of some elements in a Bureau of Standards stainless steel sample are compared in Table X with the values calculated from the mass spectra of the sample. The calculations were performed as outlined in Table I, using data from the singly charged ion lines only. Precision studies show that the analytical data were reproducible to within 25%. Larger inaccuracies are seen in these results than in those obtained in the isotope distribution measurements (Table 11) and are consistent with the previous reports that analytical errors can be as large as factors of 3 (IO). Errors of this magnitude do not result from inaccuracy in photometry or spectrum analysis. Obviously, somewhere in the process of ionization, acceleration, and transmission through the mass spectrograph, all elements do not behave alike. RELATION OF SPECTRUM TO SAMPLE COMPOSITION
In examining the relation of spectrum to sample composition it is convenient to start with the ion beam as it strikes the photographic plate and trace its path back through the instrument to the source. The factors which may alter the composition of the beam as it passes through each section will be discussed. The discussion considers only the Mattauch-Herzog double focusing instrument. Magnet Section. If the ion beam entering the magnet section diverges sufficiently in the z-direction, some of the ions will not strike the photographic plate, and the transmission factor for the magnet section will be less than unity. If i t is differcnt for ions of different mass, because of their different paths in the magnet section, the composition of the ion
+
III/(III VI, GaAs-2 GaSb
... ... ... ... 52 53
7%
64 64 64 54 64 55
InSb 58 57 63
In& 56 57 53 50 59 59
58
62 60
~~
Table X.
~
Analysis of Stainless Steel
(Bureau of Standards sample 442) Element
True % '
Determined %
31n
2.93 0.10
7.27 0.17
CU
S i Cr
1' Mo
Nb Fe
9.4
7. . 6_
17.2 0.035 0.07
23.8 0.037 0.05
0.019 70.2
0.011 61.0
beam will be altered. The maximum possible divergence of the beam is determined by the heights of the entrance slit and the effective aperture a t the entrance t o the magnet section. The actual divergence, which can vary between zero and this maximum value, depends on the position of the electrodes and the sparking conditions, With the present apparatus, the electrode positions cannot be accurately reproduced from one sample to another. The variation of transmission factor with ion path radius has been investigated by making several series of exposures with single element electrodes. In each series the ion path was varied from exposure to exposure by changing the magnetic field. The factor for each exposure was determined by comparing the yield a t the position of the photographic plate, measured either photographically or electrometrically, with the total ion beam monitored a t the entrance to the magnet section. Reasonably reprodiicible transmission factors were obtained when a series of exposures was made without moving the electrodes. If the electrodes were VOL 35, NO. 9, AUGUST 1963
1177
moved or replaced n ith others, honever, the factor for a given ion path radius varied afi3 much as 1 0 0 ~ oand , the variation with radius was appreciably altered. For example, in one case the ratio of transmission factors was 1.83 for ion path radii corresponding to those of ions of mass 7 and 238 at constant magnetic field. In another case this ratio mas only 1.04. Thus the error due to differences in transmission factor can reach 80%. The ratio was less than 1.1 only if the equivalent mass ratio was less than 1.6. Drift Tube between Magnetic and Electrostatic Sections. The principal factor affecting the ion beam in this tube is the occurrence of charge exchange collisions. This factor has been discussed above. Electrostatic Section. The electrostatic section exerts no mass discrimination upon the ion beam. The pressure in this section is usually kept very low, i n order t o reduce to a negligible level any collisions between ions or between ions and residual gases. Consequently the transmission factor of this section should be the same for all elements entering this section with equal energy distributions. Ion Source Section. The production of ions by spark discharge in a vacuum is not well understood. It seems likely t h a t the total process is a mixture in unknown proportions of sputtering, thermal ionization, volatilization, diffusion, electron impact ionization, and field emission. Such factors as relative ionization efficiencies of the elements, fractional volatilization, preferential diffusion, varying decomposition energies of different compounds, unequal energies and energy distributions of the ions produced from different elements, and microsegregation in the sample can influence the composition of the ion beam emerging from the accelerator. Experimentally it is difficult to determine the individual effect of each of these factors. The sensitivity factors obtained by Craig, Errock, and Waldron (6) and by Sermin (22) probably reflect the effects of the phenomena listed above. Since these phenomena are known to be influenced by the composition and crystal structure of the sample material, sensitivity factors involving them should not be considered generally applicable. Both Craig and Sermin were careful to state the matrix in which their sensitivity values were determined. Some effects of varying composition and of fractional volatilization can be evaluated from the results shown in Table IX. The yield of Ga and of I n is essentially the same for the arsenides and the antimonides. Thus the composition effect here is small. However, prolonged sparking of the GaAs cauaed 1 178
ANALYTICAL CHEMISTRY
the loss of the more volatile As from the area of sparking and resulted in Ga-rich spectra in the later exposures. The other compounds did not exhibit this behavior. Here the composition did affect the fractional volatilization. A recent paper by Hintenberger (12) stated that element concentration ratios seen in mass spectra can be greatly altered by changing the acceleration voltage-electrostatic field plate voltage relationship. This effect can be interpreted as a n indication that the ions of the elements exhibiting this effect do not have the same energy distribution as they enter the electrostatic field. Microsegregation might also contribute to the analytical error. The sample of stainless steel used for the analysis shown in Table X was a Bureau of Standards sample certified for emission spectrographic analysis by the spark excitation technique. Therefore, the composition of the bulk and the absence of gross segregation are well established. However, the discharge between l/r-inch-diameter electrodes used in emission spectroscopy sparks over a relatively large area of the sample compared to the sparking area in the vacuum spark used in mass spectrography. Consequently, microarea segregation that would affect mass spectrographic results might not be detected by the emission spectrograph. Thus the differences between observed and certified composition given in Table X might be due to microsegregation as well as the other factors listed above. However, precision studies performed by the authors on stainless steel show that the relative standard deviation for 10 replicate exposures of the same electrode pair averaged 13.5% for the 12 elements measured. For 10 exposures, each on separate electrode pairs made from the same sample piece, the relative standard deviation averaged 21.6% for the same 12 elements. It seems unlikely that microsegregation reproducible to this degree mould cause an inaccuracy of 280% (for Mo). It is apparent that little is known about the spark ion source, and the scant information that is available probably applies only to specific materials and is not generally applicable. The degree of reproducibility of some of the results suggests that analytical accuracy could be improved by empirical standardization, and indeed Craig, Errock, and Waldron ( 5 ) showed that this was possible for impurities in aluminum. Unfortunately, no acceptable standards for analysis a t the part per million level and below are available a t this time. The spark ion source must therefore be studied much more thoroughly before it Can bc used for quantitati\e t i u c allitlJ blb.
Since thib paper was prepared, Franxen and Hintenberger (9) and Koolston (23) have verified the prescrit authors’ suggestion that ions of different elements may have different energy distributions as they enter the electrostatic section. ACKNOWLEDGMENT
The authors gratefully acknowledge the editorial assistance of A. J. Strauss in the preparation of this paper. LITERATURE CITED
(1) Am. SOC. Testing Materials, Phila-
delphia, “Methods for Emission Spectrochemical Analysis,” 3rd ed., p. 23, 1960. (2) Aston, F. W., “Mass Spectra and Isotopes,” 2nd ed., p. 90, Edward Arnold, London, 1942. (3) Brown, C., Craig, R. D., James, J. A., Wilson, C. M., “Ultrapurification of Semiconductor Materials,” M. S. Brooks, J. K. Kennedy, eds., p. 279, Macmillan, New York, 1962. (4) Churchill, J. R., IND.ENG.CHEM., ANAL.ED. 16, 653 (1944). (5) Craig, R. D., Errock, G. -4., Waldron, J. D., “Advances in Mass Spectrometry,” J. D. Waldron, ed., p. 145, Pergamon Press, Xew York, 1959. (6) Dornenburg, E., Hintenberger, H., 2. Naturforsch. 16a, 676 (1961). (7) Duke, J. F., “Ultrapurification of Semiconductor Materials,” M. S. Brooks, J. K. Kennedy, ede., p. 294, Macmillan, New York, 1962. (8) Franzen, J., Hintenberger, H., 2. Naturfomch. 16a, 535 (1961). (9) Ibzd., 18a, 397 (1963). (10) Hannay, N. B., Ahearn, A. J., ANAL. CHEM.26, 1056 (1954). (11) Heath, R. L., “Table of Atomic Masses, Monograph SCR-245, Sandia Corp., Albuquerque, S. M., 1961. (12) Hintenberger, H., Arch. Eisenhuettenw. 33, 355 (1962). (13) Ilford Ltd., London, Tech. Inform. Sheet B524 (April 1953). (14) Lange, K. A., ed., “Handbook of Chemistry,” 9th ed., p. 113, Handbook Publishers, Sandusky, Ohio, 1956. (15) Lichtblau, H., Mattauch, J., Z. Phys. 117, 502 (1941). (16) Mattauch, J., Ewald, H., A’aturwissenschaften 41, 487 (1943). (17) Owens, E. B., A p p l . Spectry. 16, 148 ( 1962). (18) Owens, E. B., Rev. Sci. Instr. 32, 1420 (1961). (19) Owens, E. B., Sherman, A. hl., “Mass S,pectrographic Lines of the Elements, ’ Lincoln Laboratory, M. I. T:, Tech. Rept. 265 (1962). (20) .Perkins, G. D., Robinson, C. ,F., Willardson, R. K., Electrochemical Society Meeting, Houston, Tex., October 1960. (21) Rudloff, W., Z. iYaturforsch. 17a, 414 (1962). (22) Sermin, D. F., International Conf. on Spectrometry, College Park, Md., June 1962. ( 2 3 ) Woolston, J. R., Mass Spectrometry Conference, San Francisco, Calif., Nay 1963. (24) Woolston, J. R., RCA Laborator.ies, Princeton, N. J., private communlcation, 1962. RECEIVED for review January 25, 1963. Accepted May 20, 1963. Division of Analytical Chemistry, 141st Meeting, ACS, Washington, D. C., March 1962. The Lincoln 1,ahnratnry 1 8 nperated wlth siipport froni thc U. S. .irniy, Navy, and
Air Force.
