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On the use of the saha-eggert equation for quantitative sims analysis using argon primary ions
Surface Science 54 (1976) 553-560 0 North-Holland Publishing Company
ON THE USE OF THE SAHA-EGGERT EQUATION FOR QU~TITA~VE F.G. RUDENAUER
SIMS ANALYSIS USING ARGON PRIMARY IONS and W. STEIGER
iisterreichische Studiengesellschaftftir Atomenergie, Lemugasse IO, A-l 082 Vienna, Austria
H.W. WERNER F~ili~ Research ~~ret~ries,
Eindhoven, The ~ether~~s
Received 24 July 1975; manuscript received in final form 3 November 1975
Samples of known composition have been bombarded by Ar+ ions. The resulting secondary ion mass spectra, obtained with two different types of SIMS instruments, were used to check the validity of the Saha-Eggert equation for the case of Ar+ ion bombardment.
The thermodynamic approach to the quantitative interpretation of secondary ion mass spectra was first introduced by Andersen and Hinthorne [ 1] who made the observation that the relative intensities of singly charged positive ions emitted under 0; bombardment from a variety of multi-element samples could be fitted to the socalled Saha-Eggert equation [2,3]. Andersen’s interpretation of his experimental results was that a locally restricted plasma existed in the surface region of an ionbombarded solid which he assumed to be in a state of local thermodynamic equilibrium characterized by a plasma temperature T and electron density ne. Measuring the intensities of the emitted charged species the total concentration of each of the elements in the solid was inferred by means of a correction routine based on this Saha-Eggert equation. The fact that this correction routine yields concentration figures which are in reasonable agreement with the results of various standard analytical methods, could be confirmed in various laboratories [2,4,5]. Using two internal standards, relative accuracies of as good as 20% were quoted 121. Although good results have been obtained in applying this correction method, it is still possible that the basic process leading to secondary ion emission may be different from the one proposed by Andersen; in particular the assumption of a thermodynamic equilibrium in an ion bombarded solid and consequently the existence of a “temperature” may not be valid.
554
F.G. Riidenauer et al.1 Use of the Saha-Eggert
equation for SIMS analysis
Attempts to give an interpretation of the “parameter T” without using the concept of a complete thermodynamic equilibrium have been recently published by Werner [5] and Colligon [6]. In their first paper [l] Andersen and Hinthorne suggested that the assumption of thermodynamic equilibrium respectively the application of the Saha-Eggert correction procedure is justified if oxygen is used as the bombarding gas. This suggestion appears to get support among others from the assumption that, due to the increased electron availability in an oxygen-saturated solid surface compared to a rare gas bombarded surface, relaxation times for attainment of ionization equilibria could very well be noticeably shorter [7]. In this work we want to report results of measurements on well characterized aluminium and steel standards using Ar+ as primary ions. The measurements were carried out on two different types of SIMS instruments, the UHV ion microprobe VIMP-I [8] and an instrument of Cameca, S.A. (Type IMS 300, ref. [9]) in our laboratories at Seibersdorf and Eindhoven respectively. The goal of these investigations was to prove or disprove the applicability of Andersen’s correction procedure [l] for the case of Ar+ bombardment, by investigating if the experimental results obey the Saha-Eggert equation:
(1) Here ~2, ~5: and ne are the absolute ionic, neutral atomic and electron concentrations (in cm -3) respectively of element A, 2: and Zi the internal partition functions of ions and neutral atoms, Ei A the first ionization potential of an A atom; AL?is the lowering of the ionization potential due to plasma effects [3] and m, the electron mass. Note that AE, Zi and Zi all depend on me, although for the partition functions the dependence generally becomes noticeable only for plasma temperatures above 10,000 K [ 10,111. Following Andersen’s argumentation [2], the ratio of the peak heights of singly charged positive ions of species A and B emitted from the same sample is a function of the “parameter” T and the electron concentration me in the “plasma”. We further introduce the fractional concentrations CA = nA/q max ’
CB = ~B/r),,
>
(2)
where [2] VA = 77: + 17: + ?JA, and nmax is the maximum possible number of atoms A or B per cm3 in the matrix, for simplicity’s sake assumed to be equal. If we further neglect for the moment the formation of negative ions and molecular ions, we obtain for CA CA = &l Insertion tain [2]
+&/$&,r~.
of (3) into (1) and using the corresponding
(3) relations for element B we ob-
F.G. RiMenmer et al.,fiJse of the Sdm-Eggert
equation
farSIMS analysis
555
(4)
Assuming further that Q+ -6 no, i.e. assuming a low degree of ionization - which certainly is true for most elements at low plasma temperatures T and high electron concentrations ne - eq. (4) can be approximated by [ 1 I]
(5) Note that in this equation neither the electron concentration qe nor the reduction of the ionization potential M enters. The question however arises what kind of truncation procedure IlO] to use in the calculation of the partition functions if ne and AE are not known or used explicitly. As has been pointed out above, for low plasma temperatures, the partition functions do not depend on ne and bE for physically reasonable values of the electron concentration (ne w 1018-1022 cmw3). Since for any finite value of A,!? the partition functions remain finite it is justified to use the truncated partition functions given elsewhere [ 10,11,13]. If we consider that the measured ion current 1: - 712 and if we take B as reference element R, i.e., n$ = T& - Zi, we can write
If We further introduce
cr,A = CA/CR we obtain from (5)
z+z”
AR I+ __.~ i,A =%,A 0 + eXp zAzR
Ei,A-Ei,R kT
1.
Therefore, ifs denotes any element, in a plot
versus
Ei >s ;
(Sb)
(Saha-Eggert ionization plot) the corresponding points of all elements s should lie on a straight line. The results of measurements on aluminium and steel standards are given in tables l-3 and figs. l-4. In the tables, the third columns contain the atomic concentrations as given by the manufacturer (BAM, Berlin, West Germany for standards A3, A5, Gebr. Bijhler AG, Vienna, Austria) for steel No. 105 and NBS for steel 3L) and the fourth columns the peak height ratios (corrected only for isotopic abundance) of the elements related to the main component taken directly from the SIMS spectra. Samples A3, A5, 105 were measured on the VIMP-I microprobe at SGAE, Seibersdorf, sample 3L on the Cameca instrument at the Philips Labs.,
556
F.G. Riidenauer et
al./Use of the Saha-Eggert
equation for SIMSanalysis
Table 1 Atomic values and ion currents
(singly charged ions) Z,’ = (measured ion current I+)/(ion current 16 of reference element) of two aluminum standards manufactured by BAM (Berlin, W. Germany); concentration topic abundance; reference Sample
Element
figures in at% as specified element is Al Concentration
by BAM; ion currents
(BAM)
I;
corrected
for iso-
= P/Ii1
(at %) A3
A5
Si Al Ti V Fe Cu Zn
0.052 99.9 0.0096 0.0032 0.022 0.0051 0.0095
4.0 1.0 2.0 3.7 2.1 2.9 3.0
x 1o-4
Si Al Ti V Fe cu Zn
0.37 99.41 0.018 0.009 0.14 0.028 0.020
3.6 1.0 5.2 7.5 1.0 1.1 1.1
X 1O-3
x x x x x
X x x x x
1o-4 10-s 1o-4 1O-5 1o-5
1O-4 1o-4 1o-3 1o-4 1o-4
Table 2 Atomic concentrations values and ion currents (singly charged ions) 2,’ = (measured ion current I+)/(ion current 2; of reference element) of a steel standard of Boehler (Vienna, Austria); concentration figures in at% as specified by Boehler; ion currents correxted for isotopic abundance; reference element is Fe Sample
Element
Concentration
(Boehler)
I; = It/I;,
(at %) 105
Cr Mn Fe Ni
16.25 1.32 60.57 16.43
2.5 0.24 1.0 0.16
Eindhoven. Bombardment gas in all cases was Art, bombardment energy was 5.5 keV, primary current density = lop4 A/cm2. The corresponding Saha-Eggert
ionization plots in figs. l-4 show that the deviation of the elemental points from a straight line in all cases is less than a factor 2 and for most elements less than about 25%. The straight lines in the plots were obtained by a least squares fit through all the data points. The “plasma temperatures” T given in the figures have been calculated from the slope of these lines. Numerical values for the partition functions used to plot the diagrams have been obtained by an iterative method. In the first step an approximate temperature T was chosen to calculate .ZO/Z’. With these Z”/Zt values the
F.G. Riidenauer et al./Use
of the Saha-Eaert
equation for SIMSanalysis
557
Table 3 Atomic concentration values and ion currents (singly charged ions) I,’ = (measured ion current I+)/(ion current fit of reference element) of NBS steel standard 3L; concentration figures in at% as specified by NBS; ion currents corrected for isotopic abundance; reference element is Fe Sample
Element
3L
V Cr Mn Fe co Ni cu
Concentration
rr+ = I’/,+,
(NBS)
-
0.021 0.93 0.37 1.00 0.0039 0.13 0.0014
0.13 21.8 4.65 62.50 0.207 9.53 0.21
first ionization plot was obtained. From the slope of this ionization plot a corrected temperature value was obtained and this process was carried out repeatedly until no further significant changes in the slope of the least squares lines any more. Note that for the two aluminum samples the temperatures are approximately the same but that for the steel samples temperatures differ by a significant amount. At present it cannot be decided if this difference is due to the slightly different composition of samples 105 and 3L or to the fact that these samples were measured on different instruments with a different angle of incidence of the primary ions and a different energy bandpass; the bandpass used in the present experiments being 25 eV for the Cameca instrument and 50 eV for the VIMP-I.
Aluminium-Standard T: 12 600
A3 K
Fig. 1. Saha-.Eggert ionization plot of Al standard A3. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm’. Reference element: Al.
558
F. G. Riidenauer et ail/Use of the Saha-Eggert
log&-g)
arb.
equation for SIMS analysis
units
Cl
Aluminium-Standard
A5
-l-
-2J
I
7
6
9
8 Ei (eV)
Fig. 2. Saha-Eggert ionization plot of Al standard A5. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm’. Reference element: AI.
arb. units Steel Sample 105 Ta3600 K
\Fe
-2w
-&----5
i
@f)
Fig. 3. Saha-Eggert ionization plot of steel standard 105. Vertical axis in arbitrary units. Primary beam: Ar’, 5.5 keV, 0.1 mA/cm2. Reference element: Fe.
.
log
0
(?? f.,
arb. units Steel
Standard
f: 5900
31
K
0
-1
-2 i6
8
------TV 5
(ev)
Fig. 4. Saha-Eggert ionization plot of steel standard 3L. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm2. Reference etement: Fe.
Coticlusion. Measurements carried out under Ar+ bombardment on two different SIMS instruments on a number of samples, indicate a linear relationship between log[~~~i~~(Zo~Z’)] and the respective ionization potentials. In spite of the approximations which have been used in our calculations, eq. (31, therefore seems to be applicable to obtain fractional atomic concentration values on a semi-quantitative basis of homogeneous multi-element samples from secondary ion mass spectra also under Arf bombardment. The relatively large scatter of the experimental points around the Saha-Eggert line suggests two basic possibilities; (i) the principal assumption of LTE near the surface is correct, lack of sufficiently accurate atomic data and improper approximations however produce the deviations from the theoretical line; (ii) the concept of a (LTE) plasma near the surface is inapplicable, eq. (5) irrespective of its derivation happens to be a reasonably good fitting formula; T and me are fitting parameters without any physical meaning. Further work is needed to decide between these two interpretations. This work has been funded in part by the “Forschungsfiirderungsfonds Gewerblichen Wirtschaft”, Vienna, Austria.
der
560
F.G. Riidenauer et al./Use of the Saha-Eggert
equation for SIMSanalysis
References [l] C.A. Andersen and J.R. Hinthome, Science 175 (1972) 853. [2] CA. Andersen and J.R. Hinthorne, AnaL Chem. 45 (1973) 1421. [ 31 H.W. Drawin and P. Felenbok, Data for Plasmas in Local Thermodynamic Equilibrium (Gauthier-Villars, Paris, 1965), pp. 49 ff. [4] F.G. Rildenauer and W. Steiger, Fall Meeting of the DPG and GCV, Innsbruck, 1973. [5] H.W. Werner, Vacuum 24 (1974) 493. [6] C. Colligon, Vacuum, in print. [7] H.W. Drawin, in: Reactions Under Plasma Conditions, Vol. 1, Ed. M. Venugopalan (Wiley, New York, 1971) pp. 140 ff. [S] F.G. Rlidenauer and W. Steiger, Japan. J. Appl. Phys. Suppl. 2, Pt. 1 (1974) 383. [9] J.M. Rouberol, in: Proc. 5th Intern. Congr. on X-ray Optics and Microanalysis, Tubingen, 1968, Eds. G. Mollenstedt and K. Gaukler (Springer, Heidelberg, 1968). [lo] H.W. Drawin and P. Felenbok, Data for Plasmas in Local Thermodynamic Equilibrium (Gauthier-Villars, Paris, 1965) pp. 231 ff. [ll] W. Steiger and F.G. Riidenauer, SGAE-Ber. No. 2172, Sept. 1973, SGAE, Lenaugasse 10, A-1082 Vienna, Austria. 1121 F.G. Rildenauer, W. Steiger and R. Portenschlag, Microchim. Acta (Wien) Suppl. 5 (1974) 421. [13] W. Steiger and F.G. Riidenauer, Intern. J. Mass Spectrom. Ion Phys. 13 (1974) 411.
ON THE USE OF THE SAHA-EGGERT EQUATION FOR QU~TITA~VE F.G. RUDENAUER
SIMS ANALYSIS USING ARGON PRIMARY IONS and W. STEIGER
iisterreichische Studiengesellschaftftir Atomenergie, Lemugasse IO, A-l 082 Vienna, Austria
H.W. WERNER F~ili~ Research ~~ret~ries,
Eindhoven, The ~ether~~s
Received 24 July 1975; manuscript received in final form 3 November 1975
Samples of known composition have been bombarded by Ar+ ions. The resulting secondary ion mass spectra, obtained with two different types of SIMS instruments, were used to check the validity of the Saha-Eggert equation for the case of Ar+ ion bombardment.
The thermodynamic approach to the quantitative interpretation of secondary ion mass spectra was first introduced by Andersen and Hinthorne [ 1] who made the observation that the relative intensities of singly charged positive ions emitted under 0; bombardment from a variety of multi-element samples could be fitted to the socalled Saha-Eggert equation [2,3]. Andersen’s interpretation of his experimental results was that a locally restricted plasma existed in the surface region of an ionbombarded solid which he assumed to be in a state of local thermodynamic equilibrium characterized by a plasma temperature T and electron density ne. Measuring the intensities of the emitted charged species the total concentration of each of the elements in the solid was inferred by means of a correction routine based on this Saha-Eggert equation. The fact that this correction routine yields concentration figures which are in reasonable agreement with the results of various standard analytical methods, could be confirmed in various laboratories [2,4,5]. Using two internal standards, relative accuracies of as good as 20% were quoted 121. Although good results have been obtained in applying this correction method, it is still possible that the basic process leading to secondary ion emission may be different from the one proposed by Andersen; in particular the assumption of a thermodynamic equilibrium in an ion bombarded solid and consequently the existence of a “temperature” may not be valid.
554
F.G. Riidenauer et al.1 Use of the Saha-Eggert
equation for SIMS analysis
Attempts to give an interpretation of the “parameter T” without using the concept of a complete thermodynamic equilibrium have been recently published by Werner [5] and Colligon [6]. In their first paper [l] Andersen and Hinthorne suggested that the assumption of thermodynamic equilibrium respectively the application of the Saha-Eggert correction procedure is justified if oxygen is used as the bombarding gas. This suggestion appears to get support among others from the assumption that, due to the increased electron availability in an oxygen-saturated solid surface compared to a rare gas bombarded surface, relaxation times for attainment of ionization equilibria could very well be noticeably shorter [7]. In this work we want to report results of measurements on well characterized aluminium and steel standards using Ar+ as primary ions. The measurements were carried out on two different types of SIMS instruments, the UHV ion microprobe VIMP-I [8] and an instrument of Cameca, S.A. (Type IMS 300, ref. [9]) in our laboratories at Seibersdorf and Eindhoven respectively. The goal of these investigations was to prove or disprove the applicability of Andersen’s correction procedure [l] for the case of Ar+ bombardment, by investigating if the experimental results obey the Saha-Eggert equation:
(1) Here ~2, ~5: and ne are the absolute ionic, neutral atomic and electron concentrations (in cm -3) respectively of element A, 2: and Zi the internal partition functions of ions and neutral atoms, Ei A the first ionization potential of an A atom; AL?is the lowering of the ionization potential due to plasma effects [3] and m, the electron mass. Note that AE, Zi and Zi all depend on me, although for the partition functions the dependence generally becomes noticeable only for plasma temperatures above 10,000 K [ 10,111. Following Andersen’s argumentation [2], the ratio of the peak heights of singly charged positive ions of species A and B emitted from the same sample is a function of the “parameter” T and the electron concentration me in the “plasma”. We further introduce the fractional concentrations CA = nA/q max ’
CB = ~B/r),,
>
(2)
where [2] VA = 77: + 17: + ?JA, and nmax is the maximum possible number of atoms A or B per cm3 in the matrix, for simplicity’s sake assumed to be equal. If we further neglect for the moment the formation of negative ions and molecular ions, we obtain for CA CA = &l Insertion tain [2]
+&/$&,r~.
of (3) into (1) and using the corresponding
(3) relations for element B we ob-
F.G. RiMenmer et al.,fiJse of the Sdm-Eggert
equation
farSIMS analysis
555
(4)
Assuming further that Q+ -6 no, i.e. assuming a low degree of ionization - which certainly is true for most elements at low plasma temperatures T and high electron concentrations ne - eq. (4) can be approximated by [ 1 I]
(5) Note that in this equation neither the electron concentration qe nor the reduction of the ionization potential M enters. The question however arises what kind of truncation procedure IlO] to use in the calculation of the partition functions if ne and AE are not known or used explicitly. As has been pointed out above, for low plasma temperatures, the partition functions do not depend on ne and bE for physically reasonable values of the electron concentration (ne w 1018-1022 cmw3). Since for any finite value of A,!? the partition functions remain finite it is justified to use the truncated partition functions given elsewhere [ 10,11,13]. If we consider that the measured ion current 1: - 712 and if we take B as reference element R, i.e., n$ = T& - Zi, we can write
If We further introduce
cr,A = CA/CR we obtain from (5)
z+z”
AR I+ __.~ i,A =%,A 0 + eXp zAzR
Ei,A-Ei,R kT
1.
Therefore, ifs denotes any element, in a plot
versus
Ei >s ;
(Sb)
(Saha-Eggert ionization plot) the corresponding points of all elements s should lie on a straight line. The results of measurements on aluminium and steel standards are given in tables l-3 and figs. l-4. In the tables, the third columns contain the atomic concentrations as given by the manufacturer (BAM, Berlin, West Germany for standards A3, A5, Gebr. Bijhler AG, Vienna, Austria) for steel No. 105 and NBS for steel 3L) and the fourth columns the peak height ratios (corrected only for isotopic abundance) of the elements related to the main component taken directly from the SIMS spectra. Samples A3, A5, 105 were measured on the VIMP-I microprobe at SGAE, Seibersdorf, sample 3L on the Cameca instrument at the Philips Labs.,
556
F.G. Riidenauer et
al./Use of the Saha-Eggert
equation for SIMSanalysis
Table 1 Atomic values and ion currents
(singly charged ions) Z,’ = (measured ion current I+)/(ion current 16 of reference element) of two aluminum standards manufactured by BAM (Berlin, W. Germany); concentration topic abundance; reference Sample
Element
figures in at% as specified element is Al Concentration
by BAM; ion currents
(BAM)
I;
corrected
for iso-
= P/Ii1
(at %) A3
A5
Si Al Ti V Fe Cu Zn
0.052 99.9 0.0096 0.0032 0.022 0.0051 0.0095
4.0 1.0 2.0 3.7 2.1 2.9 3.0
x 1o-4
Si Al Ti V Fe cu Zn
0.37 99.41 0.018 0.009 0.14 0.028 0.020
3.6 1.0 5.2 7.5 1.0 1.1 1.1
X 1O-3
x x x x x
X x x x x
1o-4 10-s 1o-4 1O-5 1o-5
1O-4 1o-4 1o-3 1o-4 1o-4
Table 2 Atomic concentrations values and ion currents (singly charged ions) 2,’ = (measured ion current I+)/(ion current 2; of reference element) of a steel standard of Boehler (Vienna, Austria); concentration figures in at% as specified by Boehler; ion currents correxted for isotopic abundance; reference element is Fe Sample
Element
Concentration
(Boehler)
I; = It/I;,
(at %) 105
Cr Mn Fe Ni
16.25 1.32 60.57 16.43
2.5 0.24 1.0 0.16
Eindhoven. Bombardment gas in all cases was Art, bombardment energy was 5.5 keV, primary current density = lop4 A/cm2. The corresponding Saha-Eggert
ionization plots in figs. l-4 show that the deviation of the elemental points from a straight line in all cases is less than a factor 2 and for most elements less than about 25%. The straight lines in the plots were obtained by a least squares fit through all the data points. The “plasma temperatures” T given in the figures have been calculated from the slope of these lines. Numerical values for the partition functions used to plot the diagrams have been obtained by an iterative method. In the first step an approximate temperature T was chosen to calculate .ZO/Z’. With these Z”/Zt values the
F.G. Riidenauer et al./Use
of the Saha-Eaert
equation for SIMSanalysis
557
Table 3 Atomic concentration values and ion currents (singly charged ions) I,’ = (measured ion current I+)/(ion current fit of reference element) of NBS steel standard 3L; concentration figures in at% as specified by NBS; ion currents corrected for isotopic abundance; reference element is Fe Sample
Element
3L
V Cr Mn Fe co Ni cu
Concentration
rr+ = I’/,+,
(NBS)
-
0.021 0.93 0.37 1.00 0.0039 0.13 0.0014
0.13 21.8 4.65 62.50 0.207 9.53 0.21
first ionization plot was obtained. From the slope of this ionization plot a corrected temperature value was obtained and this process was carried out repeatedly until no further significant changes in the slope of the least squares lines any more. Note that for the two aluminum samples the temperatures are approximately the same but that for the steel samples temperatures differ by a significant amount. At present it cannot be decided if this difference is due to the slightly different composition of samples 105 and 3L or to the fact that these samples were measured on different instruments with a different angle of incidence of the primary ions and a different energy bandpass; the bandpass used in the present experiments being 25 eV for the Cameca instrument and 50 eV for the VIMP-I.
Aluminium-Standard T: 12 600
A3 K
Fig. 1. Saha-.Eggert ionization plot of Al standard A3. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm’. Reference element: Al.
558
F. G. Riidenauer et ail/Use of the Saha-Eggert
log&-g)
arb.
equation for SIMS analysis
units
Cl
Aluminium-Standard
A5
-l-
-2J
I
7
6
9
8 Ei (eV)
Fig. 2. Saha-Eggert ionization plot of Al standard A5. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm’. Reference element: AI.
arb. units Steel Sample 105 Ta3600 K
\Fe
-2w
-&----5
i
@f)
Fig. 3. Saha-Eggert ionization plot of steel standard 105. Vertical axis in arbitrary units. Primary beam: Ar’, 5.5 keV, 0.1 mA/cm2. Reference element: Fe.
.
log
0
(?? f.,
arb. units Steel
Standard
f: 5900
31
K
0
-1
-2 i6
8
------TV 5
(ev)
Fig. 4. Saha-Eggert ionization plot of steel standard 3L. Vertical axis in arbitrary units. Primary beam: Ar+, 5.5 keV, 0.1 mA/cm2. Reference etement: Fe.
Coticlusion. Measurements carried out under Ar+ bombardment on two different SIMS instruments on a number of samples, indicate a linear relationship between log[~~~i~~(Zo~Z’)] and the respective ionization potentials. In spite of the approximations which have been used in our calculations, eq. (31, therefore seems to be applicable to obtain fractional atomic concentration values on a semi-quantitative basis of homogeneous multi-element samples from secondary ion mass spectra also under Arf bombardment. The relatively large scatter of the experimental points around the Saha-Eggert line suggests two basic possibilities; (i) the principal assumption of LTE near the surface is correct, lack of sufficiently accurate atomic data and improper approximations however produce the deviations from the theoretical line; (ii) the concept of a (LTE) plasma near the surface is inapplicable, eq. (5) irrespective of its derivation happens to be a reasonably good fitting formula; T and me are fitting parameters without any physical meaning. Further work is needed to decide between these two interpretations. This work has been funded in part by the “Forschungsfiirderungsfonds Gewerblichen Wirtschaft”, Vienna, Austria.
der
560
F.G. Riidenauer et al./Use of the Saha-Eggert
equation for SIMSanalysis
References [l] C.A. Andersen and J.R. Hinthome, Science 175 (1972) 853. [2] CA. Andersen and J.R. Hinthorne, AnaL Chem. 45 (1973) 1421. [ 31 H.W. Drawin and P. Felenbok, Data for Plasmas in Local Thermodynamic Equilibrium (Gauthier-Villars, Paris, 1965), pp. 49 ff. [4] F.G. Rildenauer and W. Steiger, Fall Meeting of the DPG and GCV, Innsbruck, 1973. [5] H.W. Werner, Vacuum 24 (1974) 493. [6] C. Colligon, Vacuum, in print. [7] H.W. Drawin, in: Reactions Under Plasma Conditions, Vol. 1, Ed. M. Venugopalan (Wiley, New York, 1971) pp. 140 ff. [S] F.G. Rlidenauer and W. Steiger, Japan. J. Appl. Phys. Suppl. 2, Pt. 1 (1974) 383. [9] J.M. Rouberol, in: Proc. 5th Intern. Congr. on X-ray Optics and Microanalysis, Tubingen, 1968, Eds. G. Mollenstedt and K. Gaukler (Springer, Heidelberg, 1968). [lo] H.W. Drawin and P. Felenbok, Data for Plasmas in Local Thermodynamic Equilibrium (Gauthier-Villars, Paris, 1965) pp. 231 ff. [ll] W. Steiger and F.G. Riidenauer, SGAE-Ber. No. 2172, Sept. 1973, SGAE, Lenaugasse 10, A-1082 Vienna, Austria. 1121 F.G. Rildenauer, W. Steiger and R. Portenschlag, Microchim. Acta (Wien) Suppl. 5 (1974) 421. [13] W. Steiger and F.G. Riidenauer, Intern. J. Mass Spectrom. Ion Phys. 13 (1974) 411.