Emission yields in glow discharge optical emission spectroscopy

Specrrochrmrca Acta. Vol. 4gB. No. Prmted m Great Bntain.

10. pp

1247-1257.

05w547/93 $6.00 + .oo @ 1993 Pergamon Press Ltd

1993

Emission yields in glow discharge optical emission spectroscopy ZDENI?K WEISS LECO Technik GrnbH, Spectroscopy Division, Rudolf-Diesel-StraSe

lYRgb, 8031 Gilching, F.R.G.*

(Received 18 January 1993; accepted 2 April 1993) Abstract-Emissionyields of 13 lines of 11 elements have been determined for four matrices (Fe, Al, Ni, Cu) and for different discharge conditions in a Grimm-type glow discharge source. The results are discussed from the point of view of the concept of matrix-independent emission yields, which has been frequently used as a basis for quantification of glow discharge optical emission spectroscopy (GD-OES) in-depth profiling. Possible improvements of this model are discussed, including different background levels in different matrices and non-linearities in the emission yields as a function of the matrix composition.

1. INTRODUCTION IN GLOW discharge optical and excitation phenomena than in most of the other are treated separately also

emission spectrosocpy (GD-OES) [l, 21, the atomization are believed to be much more separated from each other methods of atomic emission spectroscopy. Therefore they in the basic formula for the spectral line intensity [3-71:

(1) where p(U,i) is the intensity of a line, A, of an element E in the matrix M, qM(U,i) the sputtering rate of the matrix M, R,(U,i) the emission yield of the line X, which is M the concentration of the element believed to be virtually matrix-independent, and CE E in the matrix M. The sputtering rate depends on the operating conditions of the glow discharge according to Eqn (2) published by BOUMANS 121: qM( u,i) = Cg i (u - uy)

(2)

where the reduced sputtering rate, Cz, and the threshold voltage, w, are constants specific to each matrix. This concept, which can be called “approximation of matrix-independent emission yields”, is particularly important for the quantitative interpretation of GD-OES depth profiles [4-141 because in in-depth analysis, unlike bulk analysis, the matrix changes substantially during sputtering. Therefore it is desirable to have a universal quantification procedure, which would be applicable to various matrices. The aim of this paper is to check the potential of the approximation of matrix-independent emission yields as a basis for a quantification procedure and to estimate the limits of its applicability for this purpose.

2. EXPERIMENTAL All the measurements reported in this paper were made using the LECO GDS 750 spectrometer described elsewhere [lo] with an 8 mm anode internal diameter glow discharge emission source. 2.1. Dependence of emission yields on the matrix (low concentration) In the first series of experiments, four different matrices (Fe, Al, Ni, Cu) were selected and emission yields of some lines were investigated as a function of the matrix. The measurements * Current address: Laboratory of GDOS-LECO Application Laboratory, Department of Metallurgy and Materials Science (KMM), University of West Bohemia, Americka 42, 306 14 PIzen, Czech Republic. 1247

1248

2.

WEISS

Table 1. Relative emission yields of selected lines in Al, Ni and Cu with iron as a reference matrix Matrix, M q(N) bd4 q,(N)&,(N) Ar flow at 700 V, 60 mA [seem] Line A km1 Mn I Si I Cr I Cr II Ni I cu I Ti I Al I co I v I MO I Pb I Pb II

Fe 6.7 1 305

403.449 288.158 425.433 267.716 349.296 327.396 365.349 396.152 345.351 411.179 386.411 283.307 220.351

Ni 9.6 1.44 336 rp %‘;‘I 0.99 1.02 1.19 1.05 1.12 0.95 0.99 1.07

1.04 0.68 1.07 1.04 0.69 0.97 0.82

Al cu 2.15 22.0 0.32 3.30 208 305 $1 %;4’ 6 1.49 1.97 1.40 1.93 1.69 1.69 1.48

1.31 1.48 1.50 1.42 2.12 0.98 1.66

1.19 1.26 1.51 0.81

2.20 1.67

1.23 2.43

3.12 2.71

ry: values determined from calibrations made at 700 V, 60 mA. sty: average values for voltage between 700 and 1300 V and for current between 60 and 160 mA. q&N): sputtering rate of the matrix M at 700 V, 60 mA.

were made at 700 V and 60 mA. The discharge voltage was kept constant and the current was stabilized by changing the argon flow (pressure). These operating conditions are reported below as the “normal” conditions. The argon flow was regulated by a mass-flow controller. The argon flow rates at normal conditions for particular matrices are listed in Table 1. The argon pressure in the source was not measured, but it is known that in this experimental arrangement the pressure is directly proportional to the flow rate. In this series of measurements, an iron matrix (low alloyed steels) was taken as a reference matrix and measurements of the signal intensities as a function of the concentration of several elements (i.e. a calibration) was performed for each matrix together with some Fe matrix samples containing these elements. From such a calibration, it is possible to determine the relative sensitivity factors. kp (between the matrix in question and iron as a reference matrix for each line included in the calibration), as a ratio of the slopes of calibration curves in both matrices (see Fig. 1):

kM=

h

AP^lW APIA@

Using Eqn (l), we have:

where e is the “relative emission yield”, i.e. the ratio of the emission yield of the line h in the matrix M and of the emission yield of the same line in an iron matrix. These ratios should be close to 1, if the above mentioned model for the signal intensity holds true. Sputtering rates, qM, necessary for using Eqn (4), were measured by weighing the sample before and after the analysis and also by the volume determination of the erosion crater by a surface scanning device. The accuracy of the relative emission yields determined in this way depends on the accuracies of the relative sensitivity factors and of the sputtering rates. For the relative error in the linear regression slope (sensitivity factors), the following expression was published 1151:

(5)

Emission yields in GD-OES

1249

(a) 0.3 /

t

0, /

/

0.2

._ : z B 2 k

0.1

0

,

1

3

2 Intensity

(arb. units)

/ /

10

I / /

I

/

I

1

2 Intensity

(arb.

3 units)

Fig. 1. (a) Calibration of the copper 327.3 nm line in a Ni matrix (crosses) and in steel (circles) at 700 V, 60 mA. (b) Calibration of the chromium 267.7 nm line in a Ni matrix (crosses) and in steel (circles) at 700 V, 60 mA: spectral interference from iron.

N is the number of experimental points and f the correlation coefficient. In the measurements reported here, we have achieved a relative error in the sensitivity factor determination in the range of 2-4% (for 5-12 samples of each matrix and for S-10 samples of the iron matrix). If one takes into account the accuracy of the sputtering rates, the relative emission yields, ?, are expected to have an error not exceeding 10%. Samples for these measurements were certified reference materials of low alloyed metals (matrices) listed above with the concentration of the matrix element not smaller than 97%. The resulting relative emission yields are presented in Table 1. where

1250

2.

WEISS

1

0

loo- 'O

-6 -

-5 -10

60-

-7 ,

I

I

500

-16 I

-18 I

I 1000 (V)

Discharge

voltage

Discharge

voltage

_

1300

(V)

Fig. 2. Error maps of the least-squares fits of the sputtering rate of nickel to (a} the Boumans formula (Eqn (2)) and (b) to a general quadratic form of current and voltage. Deviations from the calculated values in %. 2.2. Dependence

of emission yielab on discharge conditions

In the second series of measurements, emission yields were investigated as a function of the discharge conditions. For this purpose, only a few (2-3) samples of low alloyed steel, nickel and aluminium, with at least 95% of the matrix element, were used. For each of these samples, intensities of selected elements were recorded at different operating conditions of the discharge: at voltages of 700, 850, 1000, 1150 and 1300 V and at currents of 60, 80, 100, 120, 140 and 160 mA (30 points). The voltage was stabilized electronically and the current was selected by setting the argon flow rate. Sputtering rates of all the three matrices were dete~ined at 17 different points of the whole current-voltage area and resulting data were fitted to the Boumans formula (Eqn (2)). Because this approach leads to considerable non-random errors (see Fig. 2), sputtering rates were modelled by a general quadratic form of voltage and current. Emission intensities were then divided by the sputtering rates and the concentrations according to Eqn (l), to obtain emission yields. Before doing this, intensities were corrected by subtracting the background using a pure-matrix sample, if the background was higher than 5% of the intensity. Examples of typical plots of emission intensity and emission yield vs several parameters are shown in Figs 3-6. 2.3. Dependence of emission yields on the matrix (matrix elements) In the third series of experiments, two binary systems were investigated in the whole range of concentrations from 0 to 100%: Zn-Al alloys and Cu-Ni alloys. These measurements were made at the “normal” conditions. The sputtering rates of all of the samples were determined via mass loss. The emission yields were calculated according to Eqn (1). The results are presented in Figs 7 and 8.

1251

Emission yields in CD-OES

e-‘-----._

’

160 mA

t /

100 mA

60mA A__-A-A-"-A-A A----

0’

Fig. 3. Intensity

’ 400

1

,

,

I

I

1000 voltage (V)

700 Discharge

1300

vs the discharge conditions for the Si I 288.1 nm emission line in an Al sample.

A-------A

01 Fig. 4. Intensity,

’ 700

I

I

1000 Discharge voltage

I

I

13ilo (V)

iA,, of the Ar 415.2 nm line divided by the flow rate #I (pro~rtional pressure) vs the discharge conditions for the Al matrix.

to

3. RESULTS AND DISCUSSION

From TabIe 1, it is evident that for low concentrations of the analyte there are remarkable differences in relative emission yields for both of the different lines measured in the same matrix and the yields for one and the same line measured in different matrices. Extremely high values for both Pb lines in Cu and for the Pb 220.3 nm line in Al most probabfy can be explained by resonance absorption of these

1252

z.

WEISS

160 mA UO mA ‘120mA 100 mA 80 mA 60 mA

01

I

’

700

I

I

I

1000 Discharge voltage

1300 (V)

Fig. 5. Emission yield vs the discharge conditions for the Si I 288.1 nm emission line in an Al sample.

_A

A I!

.s )?

0

1.00 - $

:,

;:

x

+

2 .2

5

0

i!i .f

0.90 -

‘;; a!

i II + 0 A

0.80

1

700

Fig. 6. Ratio r$&

A 1000 Discharge voltage , = R&88,

160 mA 140mA 120 mA 100 mA 80 mA 60mA

_

1300 (V)

/R&XX , vs discharge conditions.

lines caused by iron atoms in the measurements of steel samples (the “reference” matrix: see Table 2). It is also clear that, e.g. in the case of the nickel matrix, most lines have similar emission yields as in iron, whereas in the case of ~uminium, the emission yields are substantialiy higher. To explain this phenomenon, more detailed investigations would be necessary: identical electrical parameters (voltage and current density) do not imply identical discharge conditions for different matrices; the electron densities and electron energy distribution functions (determining the excitation conditions) may be different. Moreover, owing to a different argon pressure and consequently a different diffusion constant of the sputtered atoms in the gas, the concentration or the dwelling time of these atoms in the plasma will also be different. Another effect that can play a role is redeposition: sputtering rates were determined from the weight loss of the sample.

1253

Emission yields in GBOES

(a) I

I

I ’

I

I

(

IO

0

20

40 60 Zn concentration (%)

80

100

0) I

I

I

I

I

+

0 2

+ -----____

s

._

0

0

+

+-+. Ll

0

+\Ll* _ _Typn-

-

0%

0

___lj---

II

d

2

t Zn330.2 nm 0 Al 396.1 nm

I

0

20

1

i

40

60

Zn concentration

I

80

I

100

(o/o)

Fig. 7. (a) Sputtering rate vs composition of Al-Zn binary alloys at ‘*normal” conditions. (b) Emission yields of the Zn I 330.2 and Al I 396.1 nm lines vs composition of Al-Zn binary alloys at “normal” conditions.

If the amount of the matrix element redeposited on the sample is different for different matrices, the emission yields determined in the above described way will be affected by this difference. As far as the matrix elements are concerned, it is evident from Figs 7 and 8 that the emission yields of the Al 396.1 nm line in Zn-Al alloys and of the Ni 349.2 and Ni 225.3 nm lines in Cu-Ni alloys do not depend on the matrix composition, whereas the Cu 327.3 nm line in Cu-Ni alloys exhibits self-absorption. Self-absorption of the Zn 330.2 nm line in the Zn-Al matrix is much weaker because in this case we should take into account an enormous increase of sputtering rate if the Zn concentration approaches 100%. The C 219.226 nm line exhibits a steep increase of emission yield in the vicinity of 100% Ni. The intensity of this line is most probably influenced by

z.

1254

0

1

0

,

20

WEISS

I

40

I

,

60

80

Ni concentration

0

Ll 0

20

1

I

40

60

Ni concentration

L

100

(%)

OCu 219.2nm 0 Ni 349.2nm 0 Ni 225.3nm I I 80

100

(%)

Fig. 8. (a) Sputtering rate vs composition of Cu-Ni binary alloys at “normal” conditions. (b) Emission yields of four Cu and Ni lines vs composition of Cu-Ni binary alloys at “normal” conditions.

Table 2. Spectral interferences from matrix elements in measurements from Table 1 Line A (nm)

Pb II Pb I Ti I Cr I 220.351 283.307 365.350 267.716

Interfering line A (nm)

Fe Fe II Fe I Fe 220.346 283.310 365.376 267.687

Emission yields in GD-OES

interference from the Ni line at 219.212 nm and therefore difficult to explain.

1255

its behaviour

is more

3.2. Dependence of the em&ion yielak on the discharge parameters A typical plot of the emission yield vs the discharge conditions is presented in Fig. 5. At a constant voltage, emission yield was found to increase linearly with the current (current density). An interesting point is that, unlike the intensity of an argon line (see Fig. 4), the emission yield of the analytes decreases with increasing voltage if the current is kept constant. This phenomenon can be connected with changing pressure and consequently with changing diffusion coefficients of sputtered atoms in the plasma. In the emission line-matrix combinations considered (eight lines in three matrices: 24 data sets), there was no exception from this rule. Emission yields of the same line in different matrices as functions of the discharge voltage and current were found to be directly proportional to one another over the whole range of the current and the voltage investigated. Standard deviation of the ratio

was typically 5% and for no combination of X and M it exceeded 10% (see Fig. 6). Average values of the ratio given by Eqn (6), denoted CRY,are summarized in Table 1, together with corresponding factors determined for a single point, namely 700 V, 60 mA, from the slopes of calibration curves. 4. SOME MODELS FOR THE EVALUATION OF GD-OES

DATA

As a starting-point for the evaluation of GD-OES data, we take the simple assumption that the emission yields are independent of the matrix. Accordingly, the calibration and quantification procedures are as follows. During the calibration, reference samples are measured at some standardized operating conditions, e.g. at the “normal” conditions as defined in Section 2.1. The intensities of all the lines included in the calibration (and measured simultaneously) are divided by the sputtering rates of the reference samples and the resulting quantities are plotted against the certified concentration values to obtain the calibration curve. According to Eqn (l), we have:

P(N)

m

R,(N) &’

=

(7)

which means that the quantity that we are determining as the slope of the calibration curve is the emission yield of the emission line in question. The symbol “N” in Eqn (7) is a symbol for “normal” operating conditions. Now, the same equation that describes the calibration holds also for the analysis of an unknown sample, if the analysis is performed at “normal” conditions. To apply this equation to the determination of concentrations, the sputtering rate q&N) of the unknown sample must be first evaluated. This is done by normalizing the concentrations to 100% (= l), provided that virtually all the elements present in the sample are being analysed: qM(N) =

c @?fi A

Ri (NJ .

Now, let us suppose that the analysis (not the calibration) normal conditions. From Eqn (1) we have:

(8) was made at other than

1256

z.

WEISS

Let us suppose that we know for each of the emission lines the dependence of the emission yield on the operating conditions:

fx( U,i)

Then, it is possible to use the same procedure based on Eqns (8a) and (9) for determining both the sputtering rate, qM(U,i), of the analysed sample and its composition, because the emission yields, R,(N), are known from the calibration:

By integrating the sputtering rate as a function of the sputtering time, we can also convert the time-scale into a depth scale. If the sputtering rates are expressed in mass per unit time @g/s), the density as a function of composition must be known, which can be sometimes a problem. In this way, it is possible to quantify the depth profile only by using bulk calibration samples, for which, in addition to the composition, the sputtering rates at “normal” operating conditions should be known. The first systematic study on GD-OES quantification was published by BENGTSON [4]. He introduced corrections of the emission intensities with respect to the discharge voltage and current and wrote a program for the GD-OES quantification [S], which has become a model for most of the currently used quantification software packages. However, his approach differs a little from the above presented model, because Bengtson’s voltage and current corrections are applied directly to the measured intensities and not to the emission yields. The above presented model, including the sputtering rate determination by normalizing the concentrations up to lOO%, was decribed by a group of French researchers [3, 6, 71. A similar model, applied to the analysis of Zn-Fe galvanic coatings, was developed at Nippon Steel Corp. [8, 91. From the results presented in Section 3, it is evident that the basic quantification model has serious limitations, especially for the analysis of elements at low-concentration levels. On the other hand, this model can be modified in such a way as to describe reality more accurately, and, because of a high reproducibility of the analysis, the modified model has a potential of giving better results than the currently used model. To show a possible modification of the basic model, let us suppose that we are analysing a thin film-substrate system consisting of an element A as the substrate and an element B as the coating, with a diffusion zone at the interface and with a presence of low-concentration elements (analytes) in both matrices. Then, instead of Eqn 1, we can write for the emission intensity Zh,x of the line A of the low-concentration analyte X at any point of the depth profile: k,X

=

qM

(Rf,XCA

+

@,XcB)

CX

+

(B?.XCA

+

B:$B)

(11)

where R?,x is the emission yield of the line A in the matrix of element A and Bex is the background intensity of this line in the same matrix. The corresponding quantities with upper index B refer to the matrix of element B. All these quantities can be simply determined by calibrations similar to those displayed in Fig. 1. To include the background terms is particularly important if there is a spectral interference from the matrix element(s) (Fig. l(b)). F or matrix element A, we can write: IA,, = qM R,,, (CA&B)CA + and for element B, an analogous versa. In most cases, the function

equation

%‘,ACB

with “A” substituted

R h.A - RA,A(CAJB)

(12) by “B” and vice-

(13)

Emission yields in GD-OES

1257

will be constant, as shown for both nickel lines in Fig. 8(b) and for the aluminium line in Fig. 7(b). The most important reason for a possible non-linearity seems to be self-absorption of the line or interference from a line of another matrix element. Generalization to several matrix elements is straightforward. Now, instead of several independent linear equations, (8) and (9), we have a generally non-linear set of equations, (8a), (11) and (12), for each point of the depth profile. The functions at Eqn (13), describing the matrix-dependence of the emission yields, should be determined experimentally as presented in Figs 7(b) and 8(b). For solving the system of Eqns @a), (11) and (12), various iterative methods can be used. Because a strong non-linearity is expected only for one or two variables (matrix elements), it is desirable to “tailor” the computation for the specific application for which the quantification procedure is being developed rather than to use a general scheme for solving non-linear systems of equations.

5. SUMMARYAND CONCLUDINGREMARKS The aim of this work was to describe phenomenologically the GD-OES analysis in terms of the approximation of matrix-independent emission yields. It was found that this approach can be used as a first approximation for such a description, but it is generally not sufficient for a correct quantitative evaluation of the experimental GD-OES depth profile data. By a proper choice of the emission lines for the matrix elements [16, 171, it is possible in most cases to avoid non-linearities in the description and to correct for the matrix-dependence of the emission yields and the matrixdependence of the background intensities only for low-concentration and trace elements. In this way, it is possible to achieve substantial improvements in the quantification of the GD-OES depth profile data and to approach the accuracy achievable so far only in the (bulk) analysis of samples with a very similar matrix. Acknowledgements-The

author wishes to thank to M. ANALYTISand H. BBHMfor many fruitful discussions

on the subject.

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Surf. Interf. Anal.

6, 174 (1984). [4] A. Bengtson,

Spectrochbn. Acru 4OB, 631 (1985). [S] A. Bengtson and A. Eklund: P,Q-sojiware for quantitative evaluation and graphical presentation of CD-UES depth profiles-User’s manual. Swedish Institute for Metals Research, Stockholm (1991). (61 J. Pons-Corbeau, Surf, lnterf. Anal. 7, 169 (1985). (71 J. Pons-Corbeau, J. P. Cazet, J. P. Moreau, R. Berneron and J. C. Charbonnier, Surf. Interf. Anal. 9, 21 (1986). (81 K. I. Suzuki, T. Ohtsubo and T. Watanabe, Nippon Steel Technical Report 33, 36 (1987). (9) K. Takimoto, K. Suzuki, K. Nishizaka and T. Ohtsubo, Nippon Steel Technical Report 33, 28 (1987). [lo] Z. Weiss, Specrrochim. Acra 47B, 859 (1992). [ll] A. Bengtson, A. Eklund, M. Lundholm and A. Saric, J. Anal. At. Specrrosc. 5, 563 (1990). [12] K. Tsuji and K. Hirokawa, Surf. lnterf. Anal. 17, 819 (1991). [13] D. Fang and R. K. Marcus, J. Anal. At. Spectrosc. 3, 873 (1988). [14] H. Nickel, W. Fischer, D. Guntur and A. Naoumidis, J. Anal. At. Spectrosc. 7, 239 (1992). (151 J. Higbie, Am. J. Phys. 46 (9) 945 (1978). [16] A. N. Zaidel, V. K. Prokofev, S. M. Riskii, V. A. Slavnyi and E. Ya. Shreider, Tublirsy spekrral’nych linii. Nauka, Moscow (1969). [17] A. R. Striganov and N. S. Sventickii, Tablirsy spekrrul’nych linii nejtrul’nych i ionizovannych aromov.

Atomizdat,

Moscow (1966).