Anal. Chern. 1985, 57, 1636-1643
itm
overall Py-MS technique is an exciting analytical tool for the forensic scientist.
LITERATURE CITED Wooiey, W. D. Br. Polym. J . 1972. 44, 27-43. Hiieman, F. D.; Voorhees. K. J.; Wojcik, L. H.; Birky, M. M.; Ryan, P. W.; Elnhorn, I. N. J. Polym. Sc/., Polym. Chem. Ed. 1975, 13,
571-584.
Meuzelaar, H. L. C.; Haverkamp, J.; Hlleman, F. D. “Pyrolysis Mass Spectrometry of Recent and Fossil Blomaterlals”; Compendium and Atlas; Elsevler: Amsterdam, 1982. Irwln, W. J. ”Analytical Pyrolysis, A Comprehensive Guide”; Marcel Dekker: New York, 1982. Voorhees, K. J., Ed. ”Analytical Pyrolysis, Techniques and Applications”; Butterworths: London, 1984. Tsao. R.; Voorhees, K. J. Anal. Chem. 1984, 56, 368-373. Babrauskas, V. “Development of the Cone Calorimeter - A Bench Scale Heat Release Rate Apparatus Based on Oxygen Consumption”; U.S. Department of Commerce, National Bureau of Standards, Center for Fire Research: Washington, DC, 1982; NBSIR 82-281 I . Giacobbo, H.; Slmon, W. Pharm. Acta Helv. 1984, 39, 162-167. Tsao, R.; Voorhees, K. J. Anal. Chem. 1984, 56, 1339-1343. Kowalskl, B. R.; Bender, C. F. J. Am. Chem. SOC. 1972, 9 4 , 5832.
(11) Mallnowski. E. R.; Howery, D. G. “Factor Analysls In Chemistry”; Wiley: New York, 1980. (12) Sammon, J. W. I€€€ Trans. Comput. 1989, C-18, 401. (13) Kowalski, B. R.; Bender, C. F. J. Am. Chem. SOC. 1973, 9 5 , 686-693. (14) Fukunaga. K.; Koontz, W. L. G. IEEE Trans. Comput. 1970, C-19, 311. (15) Rummel, R. J. “Applied Factor Analysis”; Northwestern University Press: Evanston, IL, 1970. (16) Catell, R. B. “Factor Analysis”; Harper and Brothers: New York,
1978. (17) Harper, A. M.; Duewer, D. L.; Kowalski, B. R.; Fashing, J. L. “Chemometrlcs: Theory and Applications”; Kowalski, B. R., Ed.; American Chemlcal Society: Washington, RC, 1977; ACS Symp. Ser. 52, p 14. (18) Madorsky, S. L. ”Thermal Degradatlon of Organic Polymers”; Wley-Intersclence: New York, 1964. (19) Windig, W.; Meuzelaar, H. L. C. Anal. Chem. 1984, 56, 2297-2303.
RECEIVED for review January 22,1985. Accepted March 29, 1985. This work has been supported by the Center for Fire Research of the National Bureau of Standards, Grant No. NBS 1NADA2020.
Cross Calibration of Secondary Ion Mass Spectrometers Friedrich Rudenauer* and Wolfgang Steiger Austrian Research Center Seibersdorf, Lenaugasse 10, A-1082 Vienna, Austria Miklos Riedel Eotvos Lorand University, Department of Physical Chemistry, Puskin u. 11-13, H - 1088 Budapest, Hungary Horst E. Beske and Horst Holzbrecher K F A Julich, ZCH, Pf. 1913, 0-5170 Julich, Federal Republic of Germany Heinz Dusterhoft Humboldt University of Berlin, Physics Section, Invalidenstrasse 41, DDR-1040 Berlin, German Democratic Republic Michael Gericke, Carl-Ernst Richter, Michael Rieth, and Manfred Trapp V E B Werk f . Fernsehelektronik, Ostendstrasse 1-5, Berlin, German Democratic Republic Janos Giber and Andras Solyom Technical University of Budapest, Physics Institute, Budafoki ut 8, H-1111 Budapest, Hungary Hermann Mai Akademie d. Wissenschaften, ZFW, Helmholtzstrasse 20, 8027 Dresden, German Democratic Republic Gerhard Stingeder Technical University Vienna, Institute of Analytical Chemistry, Getreidemarkt 9, A - 1060 Vienna, Austria I t Is known from prevlous round-robin experiments that relative sensltlvity factors, obtained on Identical samples by different SIMS Instruments, frequently dlsagree by a factor of up to 50. A method Is suggested for cross-calibrating lnstruments In such a way that relative elemental sensitlvity factors determlned on one SIMS Instrument may be used on another Instrument for quantlficatlon of unknown samples. The method conslsts In actlvety tuning the operatlng parameters of Instruments in such a way that relatlve sensltivlty factors for 6 and W (wlth respect to Fe) in a homogeneous B,,Fe,,W,o metaillc glass sample (“prlmary callbratlon standard”, PCS) are In close agreement on ail particlpating Instruments. I n an experlment In whlch thls cross-caiibratlon strategy has been adopted, relathre senstllvity factors of seven further elements, determined on seven different SIMS Instruments (including ion microscopes, ion mlcroprobes, and quadrupole-SIMS), agree within a factor of the order of 1.7. Improvements may be expected wlth better tuning to the PCS.
It has been and still is a matter of considerable concern that quantitative analytical results, obtained on different SIMS instruments on the same samples, do not correlate well at all. A number of round-robin analyses on a selection of wellcharacterized homogeneous samples (1-3) indicated that raw data (peak height ratios) might deviate by a factor of up to 50 and that element concentrations, derived from the raw data using customary quantification algorithms (sensitivity factors or LTE-type correction), still deviate by a factor of the order of 5 (2). The presently still unsatisfactory status of SIMS quantification models ( 4 ) might have contributed to the bad correlation of quantified results, but the tremendous differences in the raw data clearly indicate that the main effort has to be put into standardization of instrument tuning and operating conditions. The lack of correlation of analytical results has two main consequences: (a) the analytical accuracy of quantitative results obtained by SIMS is considered not to be very high (with notable exceptions in simple matrices such as ion-im-
0003-2700/85/0357-1636$01.50/00 1985 Amerlcan Chemlcal Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
planted semiconductors); (b) in the frequently used relative sensitivity factor (RSF) quantification model, a transfer of RSF data between instruments is impossible. This means in a practical situation that for each element which has to be quantitatively determined in a particular matrix type by a particular laboratory (instrument), the workload of determining the respective RSFs completely remains with that particular laboratory. Considering, that in a general analytical facility of the order of 60 elements might have to be determined in maybe 20 different matrices, the determination of all the respective RSFs might be too great a job to be performed on a single instrument. This paper describes a method which should allow transfer of relative sensitivity factors between individual instruments thus allowing splitting up the workload of determining “universally” applicable relative sensitivity factors. T r a n s f e r of Relative Sensitivity F a c t o r s between Different SIMS Instruments. Method of Constant Relative Sensitiuity Factors. When elements Xi and R are present in a sample with concentrations c(Xi) and c(R), respectively, their peak height ratio I(Xi)/I(R) in the SIMS spectrum can be expressed by the “fundamental” SIMS formula (5, 6), provided sputtering equilibrium has been obtained. T(&) - - ----- Ybt (1) I@) c(R) Ybt a@) T(R) where Ybtis the sputtering yield of the sample, a(XJ and a(R) are the degree of ionization (number of i ions sputtered/total number of sputtered i atoms) for elements Xi and R, respectively, and T(XJ and T(R) are the transmission of the analyzer system (number of ions detected/number of ions emitted) for elements Xi and R, respectively. The last three factors in eq 1 are combined into the “relative sensitivity factor” RSF (Xi) of element Xi with respect to “reference element” R
When the relative sensitivity factors RSF(XJ of all elements present in a sample are known, the concentration of any element Xi in that sample can be determined from the peak heights I(Xi) using the well-known formula (6, 7) c(XJ =
/RSF(Xi) CiV(Xi)/RSF(Xi)J
(3)
In a formula of the type in eq 1 the factors are not strictly separable and depend, in a not fully understood manner, on a number of experimental and instrumental parameters. It may be sufficient here to say that instrumental parameters of the mass analyzer, such as position and width of the energy window, takeoff angle of the secondary ions, detector effeciency, and mass dependence of analyzer transmission are reflected in the “transmission factor” T in eq 1 and that “bombardment” parameters (e.g., energy, species, angle of incidence, and current density of primary ions) as well as “environmental” (e.g., surface coverage of reactive elements, gas pressure in the sample vicinity) and ”intrinsic” sample parameters, (e.g., chemical environment in the sample) are reflected in the degree of ionization a in (1). ”Intrinsic” sample parameters are a property of the sample and should not be influenced by the analyst. Their influence on CY and therefore on the RSF of a particular element is known as the “matrix effect” in SIMS and generally requires the determination of separate RSFs for different matrices, including those with large differences in the concentration of either the “unknown” element Xi or the reference element R. Since degree of ionization and transmission of both the “unknown” Xi and reference element R enter into the relative
1637
sensitivity factor (see eq 2), it is obvious that bombardment, environmental, and instrumental parameter sets, as defined above, will have a decisive influence on the value of the RSF of a particular element, If, therefore, either of these parameter sets is different in two particular instruments, it cannot be expected that these instruments will have identical RSFs for any chosen element. Cross-Calibration Strategy. Our new “cross-calibration” method has the following objectives: a) to find a tuning method so that instruments, even of different design, give closely corresponding raw data when identical samples are analyzed; in this case it should be possible to transfer relative sensitivity factors between cross-calibrated instruments; (b) to give an estimate of the quantificationerror when transferred relative sensitivity factors are used. It is obvious, that bombardment, environmental, and instrument tuning parameters should be identical for any two SIMS instruments in order to guarantee identical mass spectral intensity ratios and therefore “transferable” RSFs. It is relatively easy to specify a set of environmental parameters which is accessible to all participating instruments (e.g., residual gas pressure, operating pressure in the sample environment, surface coverage of active species). It is impossible to obtain a perfect match of bombardment parameters, since some of these (e.g., angle of incidence onto sample surface, energy) are fixed by the particular instrument design. Nevertheless, important parameters such as primary gas species, energy, and bombardment current density can be closely matched. The greatest difficulties may be expected in obtaining a match of tuning parameters of the mass analyzers. This is understandable if one considers the different energyand mass-transmission properties of, e.g., a quadrupole instrument and a double focusing instrument or the different extraction geometries encountered, e.g., in the “snowplow” electrode of an ARL IMMA and the immersion lens of a CAMECA instrument. It is obvious that instruments with identical positions and widths of the accepted “windows” in energy and directional distribution of secondary ions will produce identical relative sensitivity factors from a “calibration sample” under identical bombardment and environmental conditions. The reverse of this statement can be considered as the fundamental ”cross-calibration hypothesis”: if two instruments, under
identical bombarding and environmental conditions,produce identical RSFs from a calibration sample (“cross calibrated instruments”), their windows in secondary energy and directional distribution are identical; they therefore should also produce identical RSFs from samples other than the calibration sample. This hypothesis cannot claim general validity since a fit of RSFs from a limited number of elements is not sufficient to completely specify energy and directional transmission windows of instruments. It is however the philosophy of this experiment to tentatively accept the validity of this hypothesis and test the match of RSFs obtained for “unknown”elements from cross-calibrated instruments. In view of this situation we have chosen an empirical strategy of instrument tuning: (a) adjust identical environmental parameters; (b) adjust those bombardment parameters which can be adjusted to a matching set of parameters; (c) use a suitable “primary calibration standard” (PCS) sample and adjust instrument tuning in such a way that relative sensitivity factors of at least two elements contained in the sample with respect to a reference element, also contained in the sample, match as closely as possible in dl instruments participating in the cross calibration experiment. The effectiveness of the cross-calibration strategy is tested by (d) analyzing, with cross-calibrated instruments, further
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
Table I Design Parameters of SIMS Instruments participating in the Cross-Calibration Experiment' SEI primary ion species primary ion energy, keV usable primary current density, mA/cm2 primary spot size, pm primary scanning primary current, nA angle of incidence, deg takeoff angle, deg secondary acceleration voltage, V energy preselection of secondary ions mass analyzer detector
BUD
ZFW
JUE
BLE
WFB
WIE
02,N2, In, rare gas Ar
02, rare, gas 02,N2, rare gas 02, Cs, rare gas 02,N2, Cs rare O2 Nz rare gas
2-10
3-5
10-22.5
10-22.5
3-15
5.5-24.5
5.5-24.5
10-3-40
10-3-1
10-'-50
0.2-?
10-6-1
???
10-'-50
5-3000 Yes 0-70 45, 0 45, 30 2-10
300-2500 no 10-103 60
5-300 Yes 0-40
2-300 Yes
2-300 Yes 0-3000 45-25
2-300 Yes 0-3000 45-25
0
0
+4500
+4500 Yes
0
0-30 0
20
45 +1500
45 +1500
100-2000 no 0-104 45, var. 45, var. 0-30
Yes
limit.
Yes
Yes
Yes
yes
QUAD RIBER SQ 156 13 st. Cu/Be
QUAD BALZERS QMG3ll 17 st. Cu/Be
DFOC ARL IMMA I/el conv.
DFOC ARL IMMA I/el conv.
QUAD UNITRA QMS 500 13 st. Cu/Be
3
16.5(+) 28.5(-) Yes Yes 10-8
DFOC DFOC CAMECA CAMECA IMS3F IMS3F channel plate, Faraday, 17-st. Cu/Be
16.5(+) 28.5(-) Yes yes 10-8
2.5
???
???
Yes Yes 10-8
Yes Yes 5 x 10-9
Yes Yes 5 x 10-9
5 x 10-72 x 10-6 1 x 10-6
5 x 10-72 x 10-6 1 x 10-6
5 x 10-8
(1-5)
(1-5)
8 x 10-6
1 x 10-6
secondary energy at 3.2 1. dynode, keV pulse count Yes dc detection Yes background pressure in 10-9 targ. ch., torr pressure with op. 10-8 source, torr 5 x 104 max. 02-backfill pressure, torr tuning variable
0
Yes no 10-9 5 x 104 3 x 10-6
SEI, BLE, WFC, WIE JUE, ZFW BUD
X
lo-'
X
lo-'
1 x 10-6
position of energy windon target potential RF/DC - ratio of quadrupole
'QUAD quadrupole mass analyzer; DFOC, double focusing mass analyzer. SEI, Austrian Research Center Seibersdorff; BUD, physical Institute, Technical University of Budapest; ZFW, Zentralinst. f. Festkorperphysik und Werkstofforschung, Academy of SciencesjDresden; JUE, Zentralabteilung f. chem. Analysen, KFA Julich; BLE, Sektion Physik, Humboldt University, Berlin; WFB, VEB Werk fur Fernsehelektronik, Berlin; WIE, Institute of Analytical Chemistry, Technical University Vienna. Table 11. Standard Operating Conditions (SOC) in Cross-Calibration Experiment BUD primary ions primary energy at target, keV oxygen pressure in sample chamber, 10" torr primary current, nA primary spot size, pm scanning av primary current density, lo-* A/cm2 diameter of precleaning raster (spot), pm precleaning depth, nm analytical raster (spot) diameter, pm analyzed area diameter, pm secondary ion acceleration voltage, V quadrupole tuning width of energy band-pass, eV
Ar+ 3.0 ??? ???
400 no 2.0 800 50 400b 400 -20 ??? ???
SEI
BLE
JUE
WFB
02+
02+
02+
02+
02+
10.0 1.0 20 200 Yes 2.0 200 50 100 100
10.0 25.0 20 600 Yes
-13.5 1.0" 20 20 Yes 2.0 200 50 100 100 -1500 n.a. open
-13.5 4.0 20 50 Yes 2.0 200 50 100 100 -1500 n.a. open
10.5 1.0 11.7 50 Yes 2.7 200 50 200 75 4500 n.a. 50
-
4.0
-0 SOC6 ???
-1200 50 600 600 20 LAM2
--
???
-
Tuning Parameter BUD rf/dc dial setting SEI BLE secondary ion energy, V JUE ZFW sample voltage, V WFB position of energy slit, eV WIE 'In the experiments on the three-component metallic glasses, JUE did not use oxygen jet. samples and determine RSFs of "unknown" elements in these samples. The degree of match in these ''unknown'' RSFs is considered a figure of merit of the cross-calibration strategy. EXPERIMENTAL SECTION Participating Instruments. The seven instruments, participating in the cross-calibration experiment, include last generation commercial instruments as well as home-made designs. Instruments are included with scanning or with static primary
ZFW
WIE 02+ 10.5 20.0 100
50 Yes 2.0 450 50 250 60 4500 n.a. 50
deflection plate P2, V sample voltage, F position of energy slit, eV Static beam.
beams and with quadrupole or double focusing mass analyzers, respectively. Detailed instrumental parameters are listed in Table 1. Standard Operating Conditions. The cross-calibration stratem outlined above reauires closelv corresaonding bombarding and sample environmenial conditions in all par3cipating instruments. It is obvious from Table I that instrument design parameters do not in all cases allow perfect standardization of these parameters. The data in Table I1 however appear to be "I
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985 WIE
1639
Table 111. Composition of METGLAS Samples of the BFeX Series
Sp , RSF
1 --
l . E 03 l . E 02 l.E 01
t
-__--ya, -------_-__ ------
-----A ___------ --_-_____ ----_ ____---SAW)
1
element nominal concn, at. % X composition c(B) c(Fe) 4x1
sample
1
1
KFKI 81112/1 KFKI 81101/1 KFKI 81097/1 KFKI 81019/1 KFKI 80/84 KFKI 80/91 KFKI 81109/1
V
Cr Ni Zr Nb Ta W
B20Fe70Vlo 21.8 B15Fe75Cr10 15.1 B15Fe75Nilo 16.0 B13.6Fe81.6Zr513.5 B,,FewNb3 17.0 BI7FeNTa3 17.0 B,,FeVsWln 15.6
74.4 74.9 73.7 81.5 80.0 80.0
73.0
3.8 10.0 10.3 5.0 3.0 3.0 11.4
Table IV. Relative Sensitivity Factors for Different Instruments for VOP Tuning tuning variable
instrument
RSF(B)
RSF(W)
TUEi
l.E-04 50
-10
100
ENERGY [eUI
Flgure 1. Dependence of practical sensitivities (-
relative sensitivity factors
(-.-e-)
- -) in [cps/nA] and
in dimensionless units for B, Fe, and
W on tuning parameter (secondary ion energy): sample, primary calibration standard B,5Fe,5W,,; instrument, WIE (CAMECA 3F), with 50 eV wide energy window; MSPs for ail three elements and VOP
marked on horizontal scale. accessible to all instruments listed in Table I and can therefore be considered "standard operating conditions" in the cross-calibration experiment. They also should be the guideline for operating parameters in any "newcomer instrument", not having participated in the present experiment, but still wanting to use cross-calibrated sensitivity factors. The choice of 02+as a bombarding species has been made because it is expected that cross-calibrated relative sensitivity factors under oxygen bombardment will be of most practical interest. Also, oxygen introduction (either via jet or by sample chamber backfill) is adopted because the sensitivity of ion yield variations to external conditions (oxygen pressure, current density) is minimized at oxygen-saturated surfaces. METGLASS Primary Calibration Standard. In the cross-calibrationstrategy outlined above, the primary calibration standard should fulfill the following requirements: (a) Elements should be homogeneously distributed so that sample composition does not change during extended bombardment (e.g., instrument tuning). In this case steady-state conditions will prevail during the complete measuring process. (b) Sample structure should be amorphous so that crystallographic effects on ion emission will be avoided (the modification of the sampling volume by ion bombardment results in a microcrystalline structure only). (c) It should not degrade or corrode easily so that the same sample may be repeatedly used. (d) It should be possible to prepare fresh samples with closely matching elemental composition. Although knowledge of sample composition is not essential for instrument tuning in the crosscalibration experiment (instruments could be tuned to give matching peak height ratios without knowing concentrations), reproducible concentrations are of advantage in minimizing matrix effects on standards from a different batch. (e) It should contain at least three elements with standardized concentrationsso that at least two independent peak height ratios may be measured. These elements should cover as wide a mass range as possible so that mass dependence of instrument transmission (in particular of quadrupole spectrometers) can be effectively cancelled out. (0 The secondary ion energy distributions of the elements contained should be sufficiently different so that relative sensitivity factors of at least two elements are sensitive to variations in energy band-pass of the instrument. This allows adjustment of the energy band-pass of a particular SIMS instrument by measuring RSFs. That this requirement is fulfilled for the primary calibration standard used in this experiment can be seen from Figure 1, where the "tuning variable" (see Table I) corresponds
VOP BUD SEI
BLE ZFW JUE WFB WIE
-
610 Skt. 25 V 34 v 1417 V 1538 V 54 eV 31 eV
2.50 X lo-'
3.35 X
1.39"
1.40 x 2.50 X 2.58 X 5.74 X 2.50 X 1.99 X 2.54 X
3.00 x 3.35 X 3.35 X 1.90 X 4.50 X 3.36 X 3.28 X
1.80 1.00 1.03 2.73 1.34 1.26 1.03
lo-' lo-' lo-' lo-'
lo-'
lo-' lo-'
aFor TUE.
directly to the position of the energy window in the SIMS spectrum. Metallic glasses of approximate composition BzoFem(with addition of a minor third element) have been chosen for these reasons. In particular, the system B10Fe75W15meets the requirements for a primary calibration standard given above. Exact specifications of the PCS sample, together with those of further metallic glass samples are given in Table 111. All these metglass samples were prepared by splash cooling of the respective liquid alloys at a rate of approximately 106K/s). The metglass samples are manufactured in the shape of strips of 20-25 pm thickness. Sample composition was verified by atomic absorption analysis; compositional homogeneity was checked by electron microprobe analysis; amorphous sample structure was verified using X-ray diffraction (8). Secondary ion yields of these samples were previously determined and compositional homogeneity has been established (9, IO).
RESULTS AND DISCUSSION Instrument Tuning. Instrument tuning was undertaken by the seven participating instruments on the B15Fe75W10 "primary calibration standard" (PCS), specified in Table IV. Standard operating conditions were set according to Table I1 and practical sensitivities Sp(ions detected/primary current and concentration) as well as relative sensitivity factors RSF for B and W with respect to Fe were recorded as a function of a single tuning variable (see Table I) RSF(XJ = S,(XJ/S,(Fe) = V+(Xi)/I+(Fe)I [dFe)/c(Xi)l (4)
Xi = B, W where I+(Xi) [counts/s] is the secondary ion current of element Xi and c(XJ [at. %/lo01 the atomic concentration of element Xi. In all instruments (with exception of BUD) the tuning variable essentially determines the position of the energy window for transmitted secondary ions. Unfortunately, the width of the energy window, which is equally important for validity of the cross-calibration hypothesis, is not well controlled in many of the participating instruments (particularly in the quadrupoles). In those instruments (CAMECAs) where an absolute calibration of the width of the energy window can
1640
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985 RSFCW)
instruments to the chosen VOP
1. E-0 1
1
log2 T E =
(l/N>Ci(log2 [RSFi
+
(B,PMD)/RSF(B,VOP)] log2 [RSFi(W,PMD) /RSF( W,VOP)]) (5)
N designates the number of participating instruments and the summation has to be carried over all participating instruments, i. Mean square averaging is used here (in contrast to linear averaging in eq 7 below) in order to obtain a conservative estimate for TUE. Now, “individual tuning error factors (TUEJ” can be computed as
+
log2 TUEi = log2 [RSF(B,PMD)/RSF(B,VOP)] log2 [RSF(W,PMD)/RSF(W,VOP)] (6)
1. E - 0 2
I
0.1
~
W’E
WFBI
I\
’”;1 BLE
,
,
,
,
,
,l o ZFWj
RSFCB)
Flgure 2. “Tuning curves” of the seven participating instruments obtained on the primary Calibration standard under standardized operating conditions: points of minimum distances (PMD) from VOP marked with open circles; maxlmum sensitivity points for boron MSP(B) marked with black circles; most MSPs outside range of figure.
be performed, it naturally also was specified in the set of standard operating conditions (see Table 11). Figure 1shows, as an example, the results of these measurements for the WIE instrument (CAMECA IMS3F). For each value of the tuning variable, there is a corresponding pair of RSFs (for B and W, respectively), tracing out a ”tuning curve” in the (RSF(B), RSF(W)Jplane. Figure 2 shows the superimposed curves of all participating instruments. It is obvious from Figure 2 that individual instruments show different behavior of the RSFs as the tuning variable is varied. This is a consequence of differing instrument design and different physical meaning of the tuning variable in individual instruments. Note however that instruments of basically “identical” design may have widely different tuning curves. In the CAMECA 3Fs (WIE and WFB) there is essentially a parallel shift of the tuning curve by a factor of -1.25 in the direction of RSF(B). Since all other environmental and ion optical parameters are kept closely identical (see also Table 11) it is suspected that his comparatively small difference is due to the detection system (e.g., different multiplier gains for B and W, probably also the simultaneous use of Faraday detector and multiplier in the same spectrum). In the IMMAS the large deviation of tuning curves most likely is due to the extreme sensitivity of the snowplow electrode to sample position. It also can be seen that there exists no set of values for the tuning parameters for which both RSF(B) and RSF(W) are identical in all participating instruments. There is however an area in the (RSF(B), RSF(W)) plane where these curves come very close to each other; the point for which the sum of perpendicular distances (in the {logRSF(B), log RSF(W)J plot) is a minimum is defined as the “virtual operating point” (VOP) of the participating SIMS instruments. Note that in Figure 2 both axes cover 1order of magnitude and are drawn on the same length scale. On any individual tuning curve, the “point of minimum distance (PMD)” from the VOP is determined graphically and is marked with a circle. To find the point of closest mutual approach of all curves, a number of “test VOPs” is selected in the (logRSF(B), log RSF(W)J plane, the individual PMDs are determined graphically, and the mean distance of individual PMDs from the test VOP is computed. Taking into account the properties of a log-log plot, this average minimum distance - can be considered as an “average tuning error factor TUE” of the seven participating
Basically, there may be more than one local minimum for TUE; in this experiment however, the final VOP chosen lies in a rather sharp TUE-minimum and average tuning error factors in other local minima are considerably larger. Table IV gives the RSFs of the virtualoperating point (VOP) and the average tuning error factor TUE obtained in this experiment. The table further contains individual RSFs and tuning errors TUEi at respective best individual VOP tuning conditions and the average tuning error factors and the values of the individual tuning parameters for the individual PMDs. Instrument tuning actually is a multivariate search process since the tuning state of an instrument also is affected by instrument parameters other than the respective tuning variables indicated in Table I. The tuning curves presented in Figure 2 actually are the result of a two-step process. In a first round of calibration runs on the PCS, standard instrument settings were used in each laboratory as the tuning variable was scanned through the accessible range. This yielded a preliminary set of tuning curves and a preliminary VOP; the average tuning error factor at this stage was considerably larger than that given in Table IV. In the second round the participants already had an idea of the RSF range accessible to all instruments and, using different settings of instrument parameters, were able to produce the tuning curves given in Figure 2 with a much closer mutual approach. Since in many instruments the exact influence of many parameter settings on position and width of the energy window are not quantitatively known, initial tuning certainly can be a matter of experimental skill and operating experience with the particular instrument. Once the final VOP has been defined however, retuning is a routine matter, using parameter settings identical with those used in the second round and varying only the single tuning variable. It is to be noted that the only instrument using nonstandard primary beam conditions (Ar+ + oxygen jet, 3 keV; BUD) neither shows abnormal behavior of the tuning curve nor is the individual tuning error TUEi, although larger than average, outside the range of individual tuning errors of instruments with standard primary beams. This may give an indication of the adaptability of the cross-calibration strategy to nonstandard bombardement conditions. Alternate Tuning Modes. The average tuning error factor TUE for “cross-calibrated” or “VOP t u n e d instruments“ (i.e., instruments tuned as closely as possible to the VOP) is astonishingly low (- 1.39) compared to previous round-robin experiments, where no particular effort has been undertaken to correlate instrument tuning and operating parameters. AS can be seen from Figure 1,a VOP-tuned instrument generally operates a t less than maximum sensitivity for B, Fe, and W. I t is interesting to investigate how the agreement between instruments would be if, as in previous round-robin experiments, individual instruments were tuned to their individual points of maximum sensitivity (“maximum sensitivity point”, MSP) for either B, Fe, or W. These points are also marked
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
-
Table V. Average Tuning Error TUE between Seven Instruments Depending on Tuning Mode -
TUE
tuning mode VOP
1.39
MSP(B) MSP(Fe) MSP(W)
6.10 3.52
6.38
in Figure 1for the WIE instrument: MSPs(B) are plotted for all instruments in Figure 2. In order to determine the degree of agreement in the RSFs for the case of “MSP tuning”, individual operating points are marked in the (log RSF(B), log RSF(W)Jplane and a “mean operating point” (MOP) is defined as the center of gravity - of these points. Again, an average tuning error factor TUE can now be defined as the antilog of the average distance between the MOP and individual operating points in the log-log plot (analogous -to eq 5). Table V gives the average tuning error factor TUE for the case of MOP tuning in comparison to VOP tuning. Obviously, when different instruments operate at maximum sensitivity, the agreement in the raw data and therefore in relative sensitivity factors is very poor. However, by adjustment of individual instrument operating parameters, it is possible to tune instruments in such a way that raw data, at least on one particular sample, agree within a factor of K1.4. As can be seen from Table V and Figure 1,analytical agreement between different instruments can generally only be obtained at the cost of individual instrument sensitivity. Numerical values for practical sensitivities and relative sensitivity losses in the VOP vs. the MSP tuned participating instruments can be taken from Table VI. Note however that
sensitivity also depends on setting of parameters which are kept constant in this study (see Table 11); the sensitivity of the CAMECA 3Fs, e.g., can be increased by a factor of about 10 if analyzed area and energy slit width are increased. Certainly, in most instruments there may be a limitation to trace element quantification at VOP tuning. In cases however where the dynamic concentration range of an element is large (e.g., in ion implanted samples), quantification may be performed under VOP tuning in the high concentration range, whereas trace amounts could be analyzed under MSP tuning using individual, not transferable, MSP/VOP sensitivity ratios determined in the high concentration range. Deviation of Relative Sensitivity Factors on CrossCalibrated Instruments. The decisive question for the feasibility of the cross-calibration strategy is, can instruments, if tuned to a VOP on a particular PCS, also give good agreement in relative sensitivity factors of “unknown” elements from samples other than the PCS. For this purpose, six of the seven instruments mentioned in Table I were retuned to the VOP coordinates (see Table IV). Subsequently RSFs of B and six “unknown” elements were determined from the additional metglass samples described in Table 111. The retuning to the VOP immediately before measurement of ”unknown” elements is necessary because of potential drift of tuning parameters over extended time intervals. Unfortunately, due to a mechanical modification in the sample chamber it was impossible for the JUE instrument to use the oxygen jet in this second series of measurements. The results reported for the JUE instrument below therefore can be expected to deviate from those of the other instruments. The measured values of RSF(X) and RSF(B) (with respect to Fe) are compiled in Table VII. It can be noted, that in this series of measurements the instruments generally were tuned a little better to the VOP than during the first series of mesurements on the PCS (see Table IV).
Table VI. Practical Sensitivities and Sensitivity Loss Factors for VOP vs. MSP Tuned Instruments
lab
tuning
BUD
VOP MSP(B) MSP(Fe MSP(W) VOP MSP(B) MSP(Fe) MSP(W) VOP MSP(B) MSP(Fe) MSP(W) VOP MSP(B) MSP(Fe) MSP(W)
SEI
BLE
ZFW
JUE
WFB
WIE
VOP MSP(B) MSP(Fe) MSP(W) VOP MSP(B) MSP(Fe) MSP(W) VOP MSP(B) MSP(Fe) MSP(W)
S,(B), cpslnh 1.0 x 1.1 x 1.1 x 1.1x
2.0 x 3.0 x 1.8 x 2.4 x
B
av
102 102
2.0 x 10’ 3.6 X 10’ 3.4 x 10’ X
103 103 103 103
6.5 x 103 9.0 x 103 1.0x 104 6.8 X lo3
1.6 X 7.0 X 2.0 x 1.8 x
102 103
0.8
9.0 x 2.4 x 2.4 x 7.0 X
2.6
lo1
1
1
4.0 4.0 3.0 X 10’
0.4 0.4 1.2
1
1
0.4 0.4 1.3
7 7 0.9
2.6
3.0 X 3.0 X 5.0 X 5.0 X
lo2
1
lo2 lo2 lo2
0.015 0.09 0.09
1 0.07
1 1
0.01
0.6 0.6
2.2 x 102 5.0 X lo2 5.0 X 10’ 1.8 X lo2
9.0 x 6.0 X 1.0x 1.0 x
S,(Fe), cpslnh S,(W), cpslnh
sensitivity loss VOP vs. MSP tuning [factor] Fe W
6.0 X lo2 7.5 x 102 7.5 x 102 7.5 x 102
102 102
103 lo6
105 105
1.0 x 106
1.2 x 106
1.2 x 108 1.0 x 108 2.0 x 104 1.1 x 105 1.1 x 105 2.0 x 104 1.0 x 104 9.5 x 104 9.5 x 104 1.0x 104
102 103 103 lo2
1.6 x 104 2.4 x 105 1.5 X loe 1.5 X lo8 5.0 X lo6
6.0 X lo8 6.0 X lo6 5.5 x 106 1.0x 105 1.1 x 108 1.1x 106 1.1 x 106
4.0 x 104 7.2 X lo5
7.2 x 105
3.0 x 104
1641
3.6
X
1
1
1
1
lo1
0.9 0.9 0.9
0.8 0.8 0.8
0.6 0.6 0.6
0.8 0.8 0.8
lo2 lo2
1
1
1
1
0.7
0.7
1.1
0.7 1.0
0.2 0.8 0.09
0.5 0.9 0.6
2.0 x 106 2.5 x 105 2.5 x 105 2.5 x 105 3.0 x 103 1.8 x 103 1.2 x 103 3.2 x 103 1.1 x 103
5.0 X lo2 5.0 X lo2 1.2 x 103
0.01
2.6 1.1 1
0.46 0.2 0.2
1
1
1
1
0.8
0.8
0.8
0.8
0.8
0.8
0.8
1.0
0.9
0.8
1 0.2
0.8
0.9
1
1
1
1
0.09 0.09 0.9
1.7 2.5 0.9
0.7 0.9 0.9
1 0.1 0.1 1.0
1
1
1
0.06 0.06 1.3
2.2
0.8 0.8
0.2
2.2
0.9
1.1
1642
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
Table VII. Relative Sensitivity Factors for Boron and Element X Obtained on PCS and “Unknown” METGLAS Samples with VOP Tuned Instruments element X
sample
SEI
TUE, KFKI 81112/1
B
V
KFKI 81101/1
B
KFKI 81097/1
Cr B Ni
KFKI 81019/1
B Zr B Nb B
KFKI 80/84 KFKI 80/91
Ta
KFKI 81109/1
B W
BLE
ZFW
JUE
WFB
WIE
1.097
1.21
2.19
1.25
1.07
1.097
0.140 1.60 0.119 2.04 0.163 0.43 0.160 0.135 0.133 0.641 0.146 0.0839
0.25 2.90
0.165 2.14
0.23 1.53 0.17 0.18
0.205 1.56 0.187 1.66 0.224 0.247 0.255 0.047 0.174 0.415 0.153 0.0312
0.124 0.60 0.102 0.042
0.141 1.71 0.134 1.89 0.121 0.487 0.145 0.243 0.138 0.98 0.129 0.055
0.168 0.943 0.163 1.20 0.167 0.483 0.222 0.654 0.207 0.551 0.145 0.0547
0.273 0.0331
0.30 0.032
0.318 0.0159
0.256 0.0318
0.235 0.0325
0.269 0.0316
Table VIII. Average Transfer Error Factors of Relative Sensitivity Factors, When Transferred between Different SIMS Instrumentsa TW”
a
source
SEI
BLE
ZFW
JUE
WFB
WIE
TE,
SEI BLE ZFW JUE WFB WIE
1 2.10 1.72 1.42 1.33 1.74
2.10 1 3.41 2.45 2.05 3.04
1.72 3.41 1 1.39 1.94 2.29
1.42 2.45 1.39 1 1.39 1.48
1.33 2.05 1.94 1.39 1 1.55
1.74 3.04 2.29 1.48 1.55 1
1.56 2.35 2.02 1.52 1.53 1.78
Global transfer error of cross-calibrationmethod, GTE = 1.68.
From Table VI1 we can derive average “transfer error factors” TRE,, between a “source” instrument s, supplying relative sensitivity factors, and a “user” instrument u, using these same relative sensitivity factors (see Table VIII). Essentially, the transfer error factor TRE,, is the ratio between the RSF for a particular element, if it were determined on the user instrument, and the RSF for that element supplied by the source instrument averaged over all Ne measured elements
Xi. Ne
log TREE,
(l/NJ Clbg (RSF,(XJ/RSFs(XJ)l i=l
(7)
Note that due to the absolute value function in eq 7, TRE,, is always larger than unity and that TRE,, = TRE,. A weighted average of TRE,, over all user instruments u gives a figure of merit TE, for a particular source instrument as a data source, and a weighted average of TE, over all source instruments gives the “global transfer error factor (GTE)”, i.e., a figure of merit for the cross-calibration experiment as such. These averages are weighted with weights g depending on the tuning error TUE of user and source instruments, respectively, since it is shown below that transfer errors are correlated to tuning errors g = l/log TUE In the present round-robin experiment, an average agreement within a fador of
