Emission yields and the standard model in glow discharge optical emission spectroscopy: Links to the underlying physics and analytical interpretation of the experimental data

Spectrochimica Acta Part B 61 (2006) 121 – 133 www.elsevier.com/locate/sab

Review

Emission yields and the standard model in glow discharge optical emission spectroscopy: Links to the underlying physics and analytical interpretation of the experimental data Zdeneˇk Weiss T LECO Instrumente Plzenˇ, spol. s r.o., Plaska´ 66, 323 25 Plzenˇ, Czech Republic Received 4 October 2005; accepted 28 November 2005 Available online 18 January 2006

Abstract The so-called standard model is a semi-empirical, physically based model describing the signal response in the glow discharge optical emission spectroscopy. Its assumptions, implications and limitations are reviewed, including links to the underlying fundamental physics. Its implementation and practical use as a calibration model in analytical applications is described, including the determination of its key parameters, the emission yields. Some data processing techniques based on the standard model are reviewed, including the multi-element calibration fitting and the signal decomposition in complex spectra. It is shown how the emission yields can be used to collect information about the glow discharge excitation. D 2005 Elsevier B.V. All rights reserved. Keywords: GD-OES; Standard model; Emission yield; Signal decomposition; Multi-element calibration fitting

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The standard model and its physical background. . . . . . . . . . . . . 2.1. Formulation of the standard model . . . . . . . . . . . . . . . . 2.2. Processes related to atomization . . . . . . . . . . . . . . . . . . 2.2.1. Cathodic sputtering . . . . . . . . . . . . . . . . . . . . 2.2.2. Transport processes in the glow discharge source . . . . 2.3. Glow discharge operation modes and glow discharge stabilization 2.4. Excitation and ionization . . . . . . . . . . . . . . . . . . . . . 2.5. Emission and the emission yields . . . . . . . . . . . . . . . . . 2.6. Self-absorption and the non-linear signal response . . . . . . . . 2.7. Other effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Implementation of the standard model . . . . . . . . . . . . . . . . . . 3.1. Basic calibration and the analysis of unknown samples . . . . . . 3.2. Sputter factors and the multi-element calibration fitting . . . . . . 3.3. Signal decomposition in complex spectra . . . . . . . . . . . . . 3.4. Precision and accuracy in the standard model . . . . . . . . . . . 4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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121 122 122 123 123 123 125 125 126 127 128 128 128 129 129 130 131 131

1. Introduction * Tel.: +420 377510811; fax: +420 377259304. E-mail address: [email protected]. 0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.11.006

Glow discharges of various kinds have been used as spectral sources for the atomic emission spectroscopy for

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Z. Weiss / Spectrochimica Acta Part B 61 (2006) 121 – 133

decades. In the late sixties W. Grimm described a glow discharge source [1] that quickly reached a great popularity among analytical laboratories. In this source, the flat sample to be analyzed functions as cathode. The cell body, a tubular anode, is at a small distance (¨0.2 mm) from the cathode and its axis is perpendicular to the cathode. A glow discharge plasma is formed inside the anode cavity and is viewed axially by an optical spectrometer. The gap between the two electrodes is shorter than the cathode dark space, which constricts the discharge to a circular area on the cathode surface in front of the anode cavity. Bombardment by energetic ions and atoms from the plasma causes atomization of the cathode surface by a process called sputtering and these sputtered atoms arrive in the glow discharge plasma. The negative glow emits a characteristic radiation (optical emission spectrum) of the discharge gas and the elements present in the sample. Analytical applications of this source involve bulk elemental analysis, mostly of metals and alloys, as well as depth profile analysis of various coatings and surface-modified materials. Over the years, many different devices employing glow discharges have been tested as spectral sources for optical emission spectroscopy [2 –8], but the Grimm-type sources are by far the most common glow discharge sources used today for routine analyses of solid materials by emission spectroscopy. Instruments based on them have been commercially available for a long time and the designation FGlow discharge optical emission spectroscopy_ (GD-OES) is almost exclusively used in connection with the Grimm-type sources. Literature about GD-OES and its applications consists of several hundred papers, including many reviews, e.g. [9 –12] and at least three monographs [13 –15]. A topic interesting to some extent to all groups involved in GD-OES is its analytical methodology, i.e. the procedures of getting analytical information by the GD-OES measurements. Information about the GD-OES methodology is scattered throughout the scientific and technical literature, instrument manuals, technical standards and other publications, frequently with a limited circulation. This review is an attempt to describe the GDOES methodology in the framework of what is sometimes called the standard model of GD-OES [19 –21], to highlight its links to the fundamental physics involved and to show how the procedures associated with the standard model are implemented. This includes also two data processing techniques, the multi-element calibration fitting [16] and the signal decomposition in complex spectra, that opened the way towards a routine use of the standard model in practice, also in connection with the instruments based on the semiconductor array detectors such as CCD. 2. The standard model and its physical background 2.1. Formulation of the standard model GD-OES is a comparative method, i.e. analytical interpretation of the GD-OES data depends on calibration. To achieve a good accuracy over a wide range of materials, the

calibration has to be ‘‘correct’’, i.e. it must correctly reflect actual relations between the signal response and the composition of the materials to be analyzed. The key to good calibrations is a correct calibration model, i.e. a correct general form of the equations linking the signal response and the composition of the analyzed material. Ideally, the calibration model should reflect in a suitable way all processes affecting the signal response, i.e. sample atomization, excitation and conversion of the emitted light into the actually measured signal(s). Various calibration models have been used in GD-OES throughout its history. It is beyond the scope of this review to discuss all those models and their ranges of applicability. Obviously, there is no Fideal_ calibration model, because physics of the glow discharge excitation is complex and not all the processes affecting the signal response are well understood. A good approximation is the scheme mentioned above and sometimes called the Fstandard model_ [19 – 21], a common platform of all data interpretation algorithms in GDOES used today. Its importance increased in the past few years with an advent of instruments using semiconductor array detectors (mostly CCD), that, unlike multichannel polychromators, cover continuous spectral ranges. With such instruments, it is possible to record large numbers of emission lines at once, quickly and with a good sensitivity. The resulting data not only contain more information about the elements present in the sample, but relative intensities of different lines of the same element reflect also various processes occurring in the spectral source. The standard model can then be used (1) as a tool to extracting this information, and (2) as a reference defining the expected Fregular_ behavior of different spectral lines and their groups. Any deviations from that Fregular behavior_ that cannot be explained within the standard model (i.e. by a proper choice of its parameters), can then be treated as matrix effects and would require additional explanation. An important quantity in GD-OES is the sputtering rate, usually denoted as q M, and defined as the amount of the material of the sample sputtered (removed) from the sample within a time unit. The sputtering rate depends on the matrix and the discharge conditions [17,18]. The index M specifies the matrix, i.e. the analyzed material. If a series of samples (materials) is analyzed, containing an element E at various concentrations c E,M, and if certain emission line k(E) of this element is recorded, its intensity I k(E),M will depend on the concentration of the element E as IkðEÞ;M ¼ RkðEÞ cE;M qM

ð1Þ

where R k(E) is a proportionality factor called the emission yield [19] of that particular line. In conformity with the indexing, and, provided that the same discharge conditions are kept throughout the whole series of measurements, R k(E) is assumed to be a characteristic of that particular line and independent of the analyzed matrix [19 – 21]. Eq. (1), together with the above definitions and statements, is the basic formulation of the standard model. A difficulty connected with this formulation is that it is not a` priori clear

Z. Weiss / Spectrochimica Acta Part B 61 (2006) 121 – 133

what it means to keep Fthe same discharge conditions_ for different samples. This point is addressed in more detail below. The standard model is by its nature a semi-empirical scheme and not all its parameters are related in a simple way to the fundamental quantities and physical parameters of the glow discharge plasma. However, it describes GD-OES analyses with a high level of accuracy in many common situations and is widely used in the analytical practice [13]. 2.2. Processes related to atomization 2.2.1. Cathodic sputtering Atomization of the sample in GD-OES occurs by cathodic sputtering, followed by a transport of the sputtered material in the excitation source. A simplified explanation of why the standard model holds is that (1) atomization in GD-OES preserves the stoichiometry of the sample and (2) excitation conditions do not depend on the cathode material. The last point is caused by the division of sputtering and excitation in space and time. Simply spoken, the atoms forgot already, where they came from and lost their bonds to the matrix. Furthermore it must be mentioned that at the place of excitation the sputtered material can be considered as strongly diluted Ar solution and the matrix becomes Ar. Let us discuss here the statement (1). A good framework for the description of what occurs on the sample surface is the concept of the sputtering equilibrium. Bombardment of the sample surface by energetic ions and atoms from the plasma causes atoms of different elements bound in the crystal lattice to leave the surface with a different probability because they have different sputter yields [22]. Hence, the flux of the sputtered atoms has a stoichiometry different from the sample surface. However, the surface becomes quickly depleted of the atoms that are sputtered away faster than the others and a very thin layer (few atomic layers) evolves on the surface, having a different stoichiometry than the bulk material. The rate of diffusion between the altered layer and the bulk of the sample is negligible, compared to the speed at which the altered layer proceeds into the depth of the sample. Because the surface is depleted of the atoms with highest sputter yields, the atoms with lower sputter yield will be relatively more abundant now, so that they will be sputtered now with a higher probability, and in the end, a stoichiometric composition of the sputtered material in the plasma is reached. This means that, after a very short initial period, the flux of the sputtered material will match the stoichiometry of the sample. The above explanation shows also that, if comparing different sample materials, the net flux U E,M of an element E entering the plasma will be equal to the product of its concentration and the sputtering rate, c E,Mq M. UE;M ¼ cE;M qM

ð2Þ

An important exception is the case of structurally inhomogeneous materials with different sputtering rates of their structural components (phases) [23,24]. If, e.g., the material consists of two phases A and B, Eq. (2) will hold for each phase separately, resulting in the following relation for the total

123

flux of the atoms of an element E entering the discharge at the beginning of the analysis: UE;M ¼ acE;A qA þ ð1  aÞcE;B qB

ð3Þ

where a is a relative coverage of the sample surface by the phase A (which is equal to its volume fraction in the material). The flux given by Eq. (3), however, generally is not in conformity with Eq. (2), if Eq. (2) is applied to the average concentration of E in the material and the Faverage_ sputtering rate of the material. Sputtering will gradually alter the relative coverage of the surface by these phases in favor of that with a lower sputtering rate, until ultimately the sputtered flux will also match the average bulk stoichiometry. The original relative surface coverage by phase A, equal to a, will be changed by sputtering into aV ag ð4Þ aV ¼ 1  að 1  gÞ where g = q B / q A. However, in this case, the transition period in which the signal of the element E will be changing will be comparable with the time needed to sputter through a typical grain of the phase with a lower sputtering rate, which can be by several orders of magnitude longer than the transition time for homogeneous materials. In a technically important case of graphitic cast irons, this time may exceed the typical time of the analysis (tens of seconds). This is an example of a structurally determined violation of the standard model that must be corrected for to achieve a correct analysis of such materials. The most common approach to such a task is to calibrate according to the standard model using structurally homogeneous reference materials (e.g. white cast irons) and then to move the calibration curve, so that it becomes compatible with a sample (or samples) of graphitic cast iron with the given structure and known concentrations of the elements to be analyzed. In the analysis of cast irons, such correction is necessary typically for carbon, sulfur and sometimes silicon. Other elements are affected only very little or not at all [24]. In the further discussion, situations in which structural inhomogenity plays a role will not be considered. 2.2.2. Transport processes in the glow discharge source Following the most common situation, in which Eq. (2) holds, it remains to show how the number density n E of the atoms of element E in the plasma depends on the cathode material. At the operating pressure of glow discharge sources, the sputtered atoms are quickly thermalized and their transport inside the source occurs by diffusion [25 – 28]. The velocity of the discharge gas flow is small compared to the thermal velocity of the sputtered atoms and its influence on the spatial distribution of n E will be therefore small [26]. In the steady state and if the gas flow velocity can be neglected, the distribution n E is described by the equation of diffusion in the following form [26]     dnE 1 B BnE B 2 nE r ¼ DE ¼0 ð5Þ þ r Br dt Br Bz2

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together with its boundary conditions, one for the sputtered area of the sample  DE

BnE ¼ u E ðr Þ Bz

at

z ¼ 0; rVR

ð6Þ

and another for the inner surface of the anode, i.e. the surface where the material originating from the sample is redeposited [27], nE ¼ 0 at r ¼ R; z > 0

ð7Þ

where D E is the diffusion coefficient and z is the axial and r the radial coordinate in a cylindrical geometry, selected so that the sample surface is in the plane z = 0, the axis r = 0 is identical with the axis of the discharge lamp and the inner surface of the anode is a cylinder r = R, z > 0 where R is the internal anode diameter. Eq. (7) assumes the sticking coefficient to be 1, i.e. that every atom of the element E coming into contact with the anode is entrapped. The function u E(r) is the radial distribution of the net flux of the sputtered atoms at sample surface, i.e. the flux of the sputtered atoms minus the backward flux of the atoms from the plasma to be redeposited on the sample surface. The total flux of the atoms of the element E entering the plasma is the integral of u E(r) over the whole sputtered area: Z R UE ¼ uE ðrÞ2krdr ð8Þ 0

Radial distribution of the net flux of the sputtered atoms is the same for every element E, except for a proportionality constant, equal to the concentration of E. Instead of describing the source of the sputtered material by the boundary condition (6) [26], a more recent approach uses an initial density profile of the sputtered material after thermalization [25,27,28]. For simplicity, we will not apply that approach here, even though it predicts the actual distribution n E(r, z) more accurately. Also effects of excitation and ionization on the transport processes in the plasma [28] are not considered. An explicit solution of Eq. (5), i.e. the spatial distribution n E(r, z) for the Grimm-type geometry, was published in [26] and a more accurate solution by computer modelling is described in [25]. A solution for the geometry of the VG9000 glow discharge cell, also obtained by computer modelling, was published in [28]. Experimental work in GDOES describing how the spatial distribution n E(r, z) is related to the observed intensities is described in [29]. The steady state of diffusion given by Eq. (5) is reached within a fraction of a millisecond (considering typical values of D E ¨300 cm2 s 1 and a characteristic thickness of the cathode fall of ¨0.1 cm [25]). Under typical conditions, the time needed to sputter one monolayer is in the millisecond range. Hence, even for the analysis of the sample surface and extremely thin layers, the steady state of diffusion is a reasonable approximation. What should be considered, however, in such applications, is the time needed to reach the sputtering equilibrium, as mentioned in the preceding paragraph. It is possible to go farther and examine how n E(r, z) depends on the sample composition. Diffusion coefficient

D E depends on the atomic mass M E of the element E [27]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 ; ð9Þ þ DE ” ME Mg where M g is the atomic mass of the discharge gas. Suppose for a minute that the transport of the sputtered material is controlled only by diffusion, not considering the process of thermalization close to the cathode. Eq. (5) and the boundary condition (7) are both linear in n E. Therefore, if certain distribution n E(r, z) satisfies Eqs. (5) and (7), so will the distribution a.n E(r, z) where a is a constant. To determine this constant and find thus the solution of our problem, we can use Eq. (6). Combining it with Eqs. (8) and (2) we get Z R BnE ðr; z ¼ 0Þ 2krdr ð10Þ cE;M qM ¼  DE Bz 0 From this, it follows that n E(r, z = 0) ” c E,Mq M / D E. But the distribution n E(r, z) is a continuous function of the spatial coordinates and the solution of Eq. (5) with the given boundary conditions is unambiguous. Consequently, n E(r, z) ” c E,Mq M / D E in every point (r, z) of the considered volume. Combining this with Eq. (9), we are getting that n E will be proportional to c E,Mq M and will depend also on the atomic mass of the element E: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ME Mg ð11Þ nE ðr; zÞ ¼ k ðr; zÞcE;M qM ME þ Mg where k(r, z) is a function independent of E and M. This is why it is the product c E,M q M that represents the element E as an independent variable in the standard model. It remains to show that Eq. (11) holds also if thermalization of the sputtered material is not neglected. In the steady state, virtually all sputtered material entering the discharge (the total net flux, see Eq. (8)) is redeposited on the anode. In analogy with Eq. (6), we can describe this by BnE DE ¼ wE ð zÞ at z  0; r ¼ R ð12Þ Br where w E(z) is the (unknown) distribution of the flux of the material to be redeposited on the anode surface. Integral of this function over the whole area where the redeposition occurs must be equal to U E, in analogy with Eq. (8). From this and following the same steps as before, we will get that n E(r = R, z) ” c E,Mq M / D E, and, from the continuity of n E(r, z) at the anode surface the relation n E(r, z) ” c E,Mq M / D E, valid in every point of the volume filled with the plasma. On the anode, however, no thermalization occurs, and no assumption concerning the thermalization close to the cathode was used. Relation (11) deserves some comments. It is not generally valid for gaseous elements, because, in most cases, these are not primarily removed from the discharge by redeposition on the cool anode surface, as expressed by Eq. (7). They are pumped away together with the flow of the discharge gas, usually argon. This may lead to a violation of the standard

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model for the elements such as hydrogen, nitrogen or oxygen, especially if the discharge is stabilized so that the pressure and consequently the flow of the working gas depends on the cathode material. It is worth mentioning that it is the relation (11) that makes GD-OES a unique technique for the direct analysis of solid samples. Comparing this example with spark excitation sources, there is no similarly straightforward correspondence in the spark between the sample composition and the number densities of different elements in the plasma. The most important reason for it is that the spark discharge causes the sample surface to melt. Evaporation is then an important atomization mechanism and the flux of the sample atoms entering the plasma depends in a complex way on the composition and the temperature of the melt (the Knudsen relation, [30]). The final remark of this section is about the sputtering rates. Note that relation (2) concerns the net flux AE,M of an element E, i.e. the sputtered flux minus the flux of the atoms of the element E coming from the plasma and redeposited on the sample surface. This makes a fundamental difference between glow discharge sputtering and the ion beam sputtering at high vacuum conditions, such as, e.g. in SIMS (secondary ion mass spectrometry) [31]. The sputtering rates q M in the glow discharge are therefore very different from the data published for the same materials for ion beam methods. Interplay between sputtering and redeposition on the sample surface is also the main cause of the crater effect in GD-OES, i.e. the fact that the erosion crater does not have a perfectly flat bottom [27,32 –35], limiting the depth resolution in the depth profiling applications. 2.3. Glow discharge operation modes and glow discharge stabilization

125

depend on the discharge current, and not so much on the pressure of the discharge gas, because the electrons, together with the ions, determine the discharge current. As far as atomization is concerned, sputtering rates depend on the discharge current i and voltage U as described by an empirical relation q ¼ Cq iðU  U0 Þ

ð13Þ

(the Boumans equation [17], C q and U 0 are constants), but not much on the discharge pressure. Therefore, in the constant voltage –constant current mode, no violation of the standard model should occur due to atomization. However, considerations like these are not clearly linked to the underlying physics and this area is still in a domain of purely empirical observations. For the rf-powered discharges, situation is even more complex. In the analysis of conductive samples, the electrical parameters that can be stabilized are the rf power delivered to the discharge and the amplitude of the rf signal or the negative dc bias of the cathode [11]. If non-conductive samples are analyzed, the dc bias cannot be measured. Moreover, the rf powering systems exhibit losses of the rf power outside the discharge, which makes their control more difficult. All those issues are addressed mainly by sophisticated hardware solutions aimed at accurate measurement, control and stabilization of the macroscopic discharge parameters [11,42 – 48]. More detailed discussion of these solutions is beyond the scope of this review. Conformity of the GD-OES signal response with the standard model must be experimentally checked for every stabilization mode and every experimental set-up. For completeness, pulsed-dc and pulsed-rf discharges [49 – 52] should also be mentioned. For pulsed discharges, there is not much information concerning the validity of the standard model. 2.4. Excitation and ionization

It was mentioned above that the second assumption for the standard model to hold is to keep Fthe same discharge conditions_ for different samples. For the dc glow discharges, there are three macroscopic operation parameters: the discharge current (or, more accurately, the current density at the cathode), the voltage and the pressure of the discharge gas (or more accurately, the density of the discharge gas). Of these three parameters, only two can be kept constant when the cathode is changing, and, depending on which two are selected, the discharge can be operated in three different stabilization modes. The equilibrium value of the third parameter depends on the coefficient of secondary electron emission of the cathode material [36,37] and the discharge gas. There was an extensive discussion in the past about how the emission intensities in GDOES depend on the macroscopic discharge parameters [38 –41], but no links have been described between these macroscopic parameters and the microscopic parameters of the plasma controlling excitation. It was empirically established that the constant voltage– constant current (U –i) mode is giving the best consistency with the standard model [13]. That is why it is the most frequently used stabilization mode for the dc discharge. The predictable signal response according to the standard model in the U – i mode is in conformity with an expectation that the electron number density in the excitation zone might mainly

Excitation and ionization of the analyte atoms in glow discharges is a fairly complex issue [10,53]. It is beyond the scope of this paper to give a complete picture of the glow discharge excitation and ionization, the aim is to focus on the aspects related to the standard model of GD-OES, i.e. discuss how excitation and ionization can be affected if the cathode matrix changes, how these changes affect the validity of the standard model and how the standard model can be used to collect experimental evidence about the corresponding changes in excitation and ionization. A glow discharge is a non-equilibrium plasma, i.e. concepts based on the local thermodynamic equilibrium (LTE) generally cannot be used. Therefore, the basic approach to describing glow discharge excitation and ionization is by computer modelling, in which all relevant processes occurring in the plasma are accounted for [10,54]. Excitation is described by collisional –radiative models, see [55]. Computer modelling has brought great progress in our understanding the glow discharge, however, until now, the systems studied by this method (e.g. pure copper in an argon plasma [56]) were relatively simple and not aimed at testing the validity of the standard model. An exception is the effect of hydrogen, on which an extensive modelling work has been done (see below).

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The standard model assumes that excitation conditions of the analyzed elements remain unaffected if the cathode material changes. Excitation and ionization is controlled by the microscopic parameters of the plasma, such as electron number density, electron energy distribution function (EEDF) and the number densities of some heavy particles such as argon ions and argon metastables. Also recombination of ions of the analyzed element and non-radiative deexcitation of its atoms and ions would have to remain unaffected to comply with the standard model. Collisions of the analyte atoms with atoms of another element sputtered from the cathode are by two or more orders of magnitude less likely than collisions with the argon atoms (with a possible exception of elements like H, O, N), but in principle also cannot be excluded as a potential cause of matrix effects. Excitation-related matrix effects in GD-OES have been reported for the situations in which light elements such as hydrogen, nitrogen and oxygen are present in the analyzed sample [57 –65]. It was experimentally established that the observed effects are similar to those caused by adding small amounts of these gases into the discharge gas. An overview of the relevant processes and some qualitative explanations for the hydrogen effects are in [66], computer modelling work on these effects is reported in [67,68]. Hydrogen was found to cause the following changes in the argon glow discharges, relevant to excitation: decrease of the electron number density, drop in the populations of argon metastables and argon ions and formation of ArH+ ions. The last effect was studied also experimentally [69]. Changes of the population of argon ions cause matrix effects in some ionic emission lines of another elements, that are known to be excited by asymmetric charge transfer (ACT) with Ar+ ions, e.g. [70,71]. Similarly, if the population of argon metastables changes, the lines of some elements excited by Penning excitation by collisions with Ar* will be affected. Also excitation-related matrix effects caused by elements heavier than H, N, O have been reported [63,72]. To describe phenomenologically the excitation-related matrix effects caused by collisional processes in the plasma with the atoms of another element, multiplicative corrections were introduced [63,73], modifying the standard model in the following way: Suppose that a line of element E is affected by an element X sputtered from the sample. Suppose that it is a collisional process in the plasma, involving atoms of the element X, that directly or indirectly depopulates or helps to populate the upper level of this line. Suppose also that if the element X is not present, intensity I k(E),M of this line is described by the standard model, Eq. (1). Then the modified expression for the intensity response of this line to the matrix changes will be Eq. (1), modified by replacing R k(E) by R k(E)(1+a k(E),Xc X,Mq M), where a k(E),X is a constant. If the upper level is depopulated by the element X, a k(E),X will be negative, if its population is enhanced in the presence of X, a k(E),X will be positive. Hence, the modified formula for the intensity response of the line E will be   ð14Þ IkðEÞ;M ¼ RE 1 þ akðEÞ;X cX;M qM cE;M qM This correction was proven for a series of Zn – Cu –Al alloys [63], having very different sputtering rates. The fact that only

the Zn II lines were subject to this matrix effect and not the Zn I lines with similar wavelengths rules out a different reflectivity of the samples to be the cause of the observed deviations from the standard model. 2.5. Emission and the emission yields By measuring the emission yields of a number of emission lines of the analyzed element, it is possible to get information about its excitation in the glow discharge. Intensity of an emission line associated with a radiative transition between states (i) and (k) of an atom can be expressed as c ni gi Aik ð15Þ Iik ¼ h kik where h is the Planck constant, c the speed of light, k ik the wavelength, n i the population of the upper level, g i its statistical weight and A ik the Einstein probability coefficient of spontaneous emission for the transition i Y k. This coefficient reflects an intrinsic atomic property and does not depend on the environment in which emission occurs. The population n i depends on the total amount of atoms n E of the respective element E available for excitation and the population factor for the state (i), f Eexc(i): ni ¼ nE fEexc ðiÞ

ð16Þ

In the LTE plasmas, excited states are populated according to the Boltzmann distribution with certain excitation temperature and the population factors can be expressed by the Boltzmann formula. For the glow discharge, this is generally not true, and the population factors depend in a complex way on the microscopic parameters of the plasma that affect the excitation/deexcitation of the level (i), see the previous paragraph. Putting together Eqs. (1), (11), (15) and (16), we get sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ME Mg c exc RE ðkik Þ ¼ j h ð17Þ AE;ik gE;i f E ðiÞ kik ME þ Mg where j is a constant. To avoid second order subscripts, emission yields are denoted as R E(k ik) instead of R k(E) in Eqs. (17) and (18). Eq. (17) can be used to check the validity of the standard model and evaluate the magnitude of its prospective violations. Suppose that A and B are two different experimental set-ups or parameters of the discharge that might lead to different excitation conditions. Let a line k ik belonging to element E be analyzed. From Eq. (17) it follows that the ratio of emission yields of the line k ik in these two matrices will be equal to the ratio of the population factors of the upper level of that line: exc fE;A ði Þ RE;A ðkik Þ ¼ exc fE;B ðiÞ RE;B ðkik Þ

ð18Þ

If the standard model holds, the ratio will be equal to 1. This approach can be used in a search for selective excitation processes, tied to specific excitation energies. An example is a study [74] in which different alloys containing titanium were analyzed in a dc discharge in pure argon and the

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R(Ar+H) / R(Ar)

1.5

1.0

Ei(H), 13.60 eV

0.5

0.0 10

11

12

13 Ek (eV)

14

15

16

Fig. 1. The ratio of emission yields of Ti II lines in the (Ar + 0.3% H2) discharge and the Ar discharge, plotted against their total excitation energy (i.e. including the Ti ionization energy). The dashed line shows the ionization energy of hydrogen. 63 Ti II lines are included in the diagram.

argon–hydrogen mixture (0.3% H2). For a number of Ti II lines, the ratio of emission yields in Ar and Ar + H2 was evaluated and plotted against the total excitation energy of the lines (i.e. the sum of the titanium ionization energy and the excitation energy relative to the Ti II ground state). The resulting plot is in Fig. 1. It is evident that adding hydrogen to the discharge gas leads to a strong violation of the standard model for most observed lines. The high values of R(Ar + H2) / R(Ar) for lines originating at the levels with an energy just below the ionization energy of hydrogen (13.60 eV) indicate that the asymmetric charge transfer Hþ þ Ti Y H þ Tiþ 4 between titanium atoms and the H+ ions is an important excitation mechanism for these levels. The data shown in Fig. 1 come from the measurements made on a CCD instrument (LECO GDS500A) and were collected using the technique of signal decomposition in complex spectra, see Section 3.3. This result is very similar to the result obtained by ratioing intensities of the same lines in the analysis of pure titanium, measured on a high resolution FTS spectrometer [74]. In the cases discussed above, we were comparing the signal of the same line in two slightly different experiments. If such measurements are made on the same instrument, there is no need to correct for the instrument response. However, if Eq. (17) is to be applied to lines at significantly different wavelengths, emission yields in Eq. (17) should be corrected for the spectral responsivity of the instrument used. Spectral responsivity, i.e. relative sensitivity of the instrument as a function of the wavelength depends on factors like the throughput of the instrument, absorption losses, reflectivity of the mirror(s) in the spectrometer, efficiency of the blazed grating and the quantum efficiency of the detector. Spectral responsivity can be measured using calibrated standard lamps, such as tungsten halogen lamp or the deuterium lamp. Emission yields corrected for the spectral responsivity of the instrument are sometimes referred to as the Fabsolute_ emission yields [73]. Using the Fabsolute_ emission yields of a set of different emission lines of an element, it is possible to look for

127

deviations from the Boltzmann distribution by the method of Boltzmann plots [76,77], in which the Fabsolute_ emission yields would be used instead of intensities. With the Fabsolute_ emission yields, it is also possible to compare relative intensities of the emission lines of different elements, with prospective applications to an analysis that would not require the conventional calibration as described below in the Paragraph 3.1. An interesting and not yet explored question is to which extent the Fabsolute_ emission yields are representative of the glow discharge source and independent of the instrument used to collect the GD-OES spectra. Also, the Fabsolute_ emission yields of lines measured on pure elements at some Fstandard_ conditions can be considered as a possible basis of a future catalogue of experimental glow discharge spectra. 2.6. Self-absorption and the non-linear signal response Self-absorption of resonance radiation occurs in the glow discharge sources and is responsible for a non-linear response of emission intensities of some lines as functions of c E,Mq M [78], i.e. for non-linear calibration curves. There is a concept, called the curve-of-growth (COG) theory [79 –81], that relates emission intensities to the optical density and can be used to calculate theoretical functions describing the experimental calibration curves. The COG of a spectral line may be calculated based on the line width, plasma parameters and the axial atom density profile of the absorbing species in the discharge cell. Line profiles can be measured, e.g. by high resolution Fourier transform spectrometry [82] and the axial atom density profiles can be calculated by computer modelling. So far, COG theory has been used largely in the laser-induced spectroscopy. There was an attempt to apply a simplified selfabsorption model to GD-OES [83], but a much more realistic approximation would be needed to get a good insight into which experimental parameters control the intensity response and in which way. For practical work, the signal response can be described by an empirically determined function f, usually a polynomial, so that, instead of Eq. (1), we have   IkðEÞ;M ¼ RkðEÞ f cE;M qM ð19Þ The asymptotic behavior at a low concentration (c E,Mq M Y 0), i.e. for the optically thin limit of COG, is given by a linear relationship similar to Eq. (1). To keep Eq. (19) consistent with the definition of the emission yield R E, Eq. (1), the function f should satisfy the condition df ¼1 dx

for

xY0;

ð20Þ

where x = c E,Mq M. It is worth mentioning that, in the range of concentrations in which a quadratic approximation is sufficient to describe satisfactorily the actual calibration curves, the function f can be chosen as f(x) = x(1 + a k(E)x), which is identical with the multiplicative correction (14) for X = E. But here, the reason for this correction is not a collisional process, but selfabsorption. Please note that Fx_ is just an independent variable of

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the function f, standing for c E,Mq M, while FX_ is a designation of the element causing the matrix effect in Eq. (14). 2.7. Other effects For completeness of the discussion of the factors that might violate the standard model, two more effects should be mentioned. First, if an inhomogeneous sample is analyzed with an instrument in which imaging of the plasma on the entrance slit of the spectrometer is not representative for the whole glowing area, analytical errors may arise due to an uneven lateral distribution of the intensities over the analyzed area [29,84]. Second, if highly reflective substrates are analyzed by GD-OES, a part of the light arising in the glow is reflected from the sample and enters the spectrometer. Intensity response will then depend on the reflectivity of the sample. If, moreover, an optically transparent thin film exists on the reflective substrate and is analyzed, the reflected light is subject to interference phenomena on the transparent thin layer. As a result, the observed intensities are modulated, because the thickness of the transparent layer is decreasing during the analysis [85,86]. This effect must be taken into account to achieve correct analytical interpretation of the data. 3. Implementation of the standard model 3.1. Basic calibration and the analysis of unknown samples In Sections 3.1–3.3, linear response of the emission intensities as functions of (c E,Mq M) will be assumed, to keep the text transparent. All concepts discussed here, however, can be generalized to the cases in which this response is non-linear. Such generalization would involve only changes in the calculus, rather technical than fundamental. Suppose that a set of samples is analyzed, which are distinguished by index M. Each of these samples contains several elements distinguished by the index E, the concentration of an element E in sample M is c E,M. Suppose that for each element, either one or several lines are recorded, denoted as k(E). The standard model, as expressed by Eq. (1), is usually amended by two additional terms in the practical work: one for line interferences and another for the spectral background b k(E): IkðEÞ;M ¼ RkðEÞ cE;M qM þ ~ skðEÞ;F cF;M qM þ bkðEÞ

ð21Þ

F

The second term on the right side arose by applying Eq. (1) to a line of an element F, adjacent to the observed line k(E), and by summing all such contributions to the total signal. Hence, the coefficient s k(E),F is a constant, independent of sample composition, and, in the case that both lines are wholly within the spectral window (i.e. if all the light coming from that line of the element F is collected), s k(E),F will be identical with its emission yield. The background term b k(E) is considered independent of the matrix. If it is not, its matrixdependent part can be put into the second term, as another line interference. The background term reflects instrumental

background, but also some real features of the spectrum, such as, e.g. molecular interferences. Suppose now that another line kV(F) of the element F is being measured, that behaves according to the standard model, Eq. (1). Then c F,Mq M can be expressed as I kV(F),M / R kV(F) and Eq. (21) can be written as IkðEÞ;M ¼ RkðEÞ cE;M qM þ ~ rkðEÞ;F Ik0 ðFÞ;M þ bkðEÞ

ð22Þ

F

where the constant r k(E),F is rkðEÞ;F ¼ skðEÞ;F =Rk0 ðFÞ

ð23Þ

The simplest case of GD-OES calibration is when the sputtering rates q M are known for all calibration samples. In such case, intensities I k(E),M and I kV(F),M are measured for all calibration samples and the parameters R k(E), r k(E),F, b k(E) can be calculated as calibration parameters by linear regression based on Eq. (22), for each line k(E) separately. As a result, we get a linear calibration curve for every line k(E) of every element E, with the product concentration * sputtering rate as independent variable, instead of just concentration, which would be a common situation in other analytical methods. When analyzing an unknown sample, intensities of analytical lines of all elements present at significant concentrations in the sample are measured and the sample composition is then determined in two steps: First, the products c E,Mq M are calculated from Eq. (22) for every element and then the sputtering rate q M is determined by summing up concentrations of all elements present in the sample: qM ¼ qM ~ cE;M ¼ ~ cE;M qM E

E

  ¼ ~ IkðEÞ;M  bkðEÞ  ~ rkðEÞ;F Ik0 ðFÞ;M =RkðEÞ E

ð24Þ

F

It was assumed that the concentrations are given as the mass- or atomic fractions and that ~E cE;M ¼ 1, i.e. all elements present in the sample were included in the sum. Eq. (24) assumes that, for every element E, only one line k(E) was used to determine the product c E,Mq M. This is a situation typical for multichannel polychromators. If more than one line is recorded for element E, a composite estimate of c E,Mq M can be used, such as, e.g. the (weighted) average of the set of the c E,Mq M-values, each of which was determined using a different line k(E) [73]. Knowing the sputtering rate q M and the products c E,Mq M, it is then straightforward to determine the sample composition. This procedure is sometimes called normalization. Instead of measuring the intensities as single values, that are supposed to be representative for the whole sample, timeresolved measurements of the intensities can be done if the sample composition is changing with depth. The same procedure as described above for the single values I k(E),M and I kV(F),M is then applied to the resulting functions I k(E),M(t), I kV(F),M(t), point-by-point, and, as a result, the sputter rate and the concentrations are obtained also as functions of time, q(t), c E(t). What remains to do to get the true depth profile, i.e. the

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composition as a function of depth, is to convert the time coordinate into depth. If the sputtering rate is expressed in the units of mass per second and x is the depth coordinate, the mass sputtered within one second will be

determined and can be solved by chi-squared fitting, minimizing the chi-squares function associated with Eq. (22),  v2 ¼ ~ ~ wkðEÞ;M IkðEÞ;M  RkðEÞ cE;M qM  bkðEÞ kðEÞ M

dm ¼ qðt Þdt ¼ pR2 qðt Þdx

ð25Þ  ~ rkðEÞ;F Ik0 ðFÞ;M

where q(t) is the density of the sample material at the depth reached by the crater bottom at the time t. The depth coordinate can be obtained by integrating the last equation, i.e. Z t 1 qð s Þ ds ð26Þ xð t Þ ¼ 2 pR 0 qðsÞ To get the density as a function of time, various approximations are used to calculate the density, based on the composition. This can be done, because, at this stage, composition is known as function of the time of sputtering and is represented by the function c E(t). 3.2. Sputter factors and the multi-element calibration fitting If only the sample composition is of interest and the information about the depth is not important, nothing will change in the calibration procedure and the analysis of unknown samples if all sputtering rates are multiplied by a common coefficient (see Eq. (21)). This allows the introduction of sputter factors, as ratios of the actual sputtering rates and the sputtering rate of a reference matrix, usually pure iron, analyzed at the same discharge conditions. The sputter factors are much less dependent on the discharge conditions than the sputtering rates (see Eq. (13) and Ref. [75]). In the following text, determination of the depth will not be of interest, which makes it possible to use the terms Fsputter factors_ and Fsputtering rates_ interchangeably. In many practical situations, the sputter factors are not known for all the calibration samples, sometimes not even for any calibration samples, or are not known with a sufficient accuracy. Also, their original purpose, i.e. to be a measure of how fast the sample is sputtered, is frequently no longer important and they become simply considered only as factors making the calibration consistent with the standard model. In cases like that, the q M factors can be defined in this way, i.e. as such values that produce the best fit of the standard model to the actually measured data. Eq. (1) then becomes a postulate and the calibration can be declared as consistent with the standard model if it is possible to find such q M factors that Eq. (1) holds for the observed intensities. Calibration parameters R k(E), r k(E),F, b k(E) in the calibration described in the preceding paragraph were calculated from Eq. (22) by linear regression, separately for each element E. That can be viewed also as solving an over-determined system of equations, one equation for every sample M. To generalize this procedure and calculate also the sputter factors as parameters of the standard model, Eq. (22) can be considered as a much bigger set of equations coupled together, namely one equation for each pair k(E), M. This system is usually strongly over-

129



2

;

ð27Þ

F

in which all the parameters R k(E), r k(E),F, b k(E) and q M are unknown variables. w k(E),M in Eq. (27) is the statistical weight of the measurement of the signal k(E) in the sample M. A mathematical method for solving this problem is described in [16]. This technique is called the multi-element calibration fitting, is implemented in the data processing software packages of most commercial GD-OES instruments and widely used at practical work. 3.3. Signal decomposition in complex spectra The formalism based on the standard model has one more practical use, especially in connection with the instruments based on semiconductor array detectors, e.g. CCDs. Such instruments cover continuous wavelength ranges, and, unlike the multichannel polychromators with photomultipliers, they offer not only one or two carefully selected Fanalytical_ lines for every element, but a significant part of the whole emission spectrum. For weaker lines in complex matrices, a difficulty arises with line interferences: in many cases, resolving power of the spectrometer is not high enough to avoid a complex signal response pattern of weaker lines, with significant contributions to the signal coming from another elements. In such cases, it is practical to start with Eq. (21) rather than Eq. (22) and treat equally all the lines that contribute to the observed spectral window (or channel), not distinguishing between the analyzed line, indexed by k(E) in Eq. (21), and the Fdisturbing_ lines of the other elements. Eq. (21) then becomes IE;M ¼ ~ sk;F cF;M qM þ bk

ð28Þ

F

where the index k denotes the affected channel. If several (or many) suitably selected channels are measured, we get the intensities I k,M for a set of samples M and every channel k. Suppose now that the sputter factors q M of these calibration samples are known. In such case, Eq. (28) is a system of linear equations for the parameters s k,F and b k , that can be solved by suitable methods of linear algebra. The parameters s k,F represent the contributions to the measured signal from different elements, hence, this procedure can be called the decomposition of the (composite) signal. It was implemented in a recent version of the GD-Tool software [16] and successfully tested. Analysis of an unknown sample will produce a set of intensities for the selected channels, and, if the (calibration) parameters s k,F and b k are known, Eq. (28) is a system of linear equations for the products c F,Mq M. These can be calculated, and the sputtering rate q M as well as the sample composition can be determined similarly as described in Paragraph 3.1. In

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Z. Weiss / Spectrochimica Acta Part B 61 (2006) 121 – 133

this way, the signal decomposition allows the complex spectra to be used analytically, without the necessity to have a Fclean_ and strong line kV(F) as a reference for the corrections of the line interferences caused by this element in another channels. This approach is useful also to collecting experimental data for fundamental studies of the GD-OES spectra: suppose that the central wavelength of the measured channel coincides with the wavelength of a spectral line F and all the light of this line is collected by the channel. Then, provided that no other lines of this element contribute to this channel, the parameter s E,F will be equal to R k(F), i.e. the emission yield of this line. Only if there is just a partial overlap of the apparent line profile (line profile broadened by all relevant mechanisms) with the spectral window of the channel, s k,F will be smaller than R k(F), and should not be used for fundamental considerations [87]. In the way described above, it is possible to get the emission yields of weak lines, and, consequently, an information that would never be accessible with such instrument, based on the intensity generated by a single sample.

Fig. 2. Decomposition of a GD-OES signal at 303.58 nm into two components: zinc (Zn I, 303.578 nm, top figure) and copper (Cu I, 303.610 nm, bottom figure). The data come from 21 Zn alloys, 8 of which also contain Cu [63]. Instrument used: LECO GDS500A, dc discharge in argon, effective spectral width of this channel was 0.07 nm. Symbol g represents the Fraw_ data, symbol D corresponds to the Fcorrected_ data (see the text).

An example of signal decomposition is in Fig. 2 [63]. The format of the plots follows the convention introduced in [16] and common in GD-OES: The Fraw_ data, i.e. the intensityversus-concentration, are depicted by squares, with the abscissa being the intensity coordinate. The Fcorrected_ data, i.e. (I E(E),M  AI k(F),M) versus (c E,Mq M) are depicted by triangles and every point of the ’raw’ data is connected with the corresponding Fcorrected_ point by a dashed line. The emission yield R k(E) is the reciprocal of the slope of the bold line. 3.4. Precision and accuracy in the standard model Uncertainty associated with the measurements interpreted by the standard model has not received much attention in the scientific literature. However, it belongs here, not only because analytical precision and accuracy is important in practical applications, but also because uncertainty associated with the experimental results is a criterion of what still can be considered in conformity with the standard model and what should be regarded as the matrix effect. For simplicity, in this paragraph, it is assumed that a single channel is recorded for each element. Hence, the element unambiguously defines the channel and index E is used instead of k(E). Propagation of uncertainty in the GD-OES analysis is described in [88]. The basic task, important especially for weaker lines, is to estimate the uncertainty dR E associated with the emission yield R E and obtained by regression from Eq. (21). General methods of how to do that can be found in [89]. If the line behaves according to the standard model, the most significant component of the resulting uncertainty are usually random fluctuations of the measured intensities, dI E,M. A crucial condition is the correct selection of the disturbing elements, indexed by F in Eq. (21). Also important is to use calibration samples with a suitable distribution of the concentrations of the element E. Ideally, concentrations of the analyzed elements should cover uniformly the respective concentration ranges and there should be no correlation between the concentrations of different elements in different samples. Uncertainty of the analyzed concentrations in unknown samples is important for analytical applications. For the medium and high concentrations for which the errors introduced by fluctuations of the background and by line interferences can be neglected, and if the analysis was made as described in Paragraph 3.1, the following result applies: if the uncertainties dI E,M and dR E are random and independent, the error dc E,M of the analyzed concentration will be given by the equation [88] "      # 2 dIE;M 2 dcE;M 2  dRE 2 ¼ 1  cE;M þ cE;M IE;M RE "    # dIF;M 2 dRF 2 þ þ ~ ð29Þ IF;M RF FmE Index F counts all the elements other than E. In multiple analyses of a single sample, only the intensities are changing,

Z. Weiss / Spectrochimica Acta Part B 61 (2006) 121 – 133

hence, the first term in each square bracket represents the random error and the second term the systematic error due to the (biased) emission yields used for the calculations, i.e. the systematic error within the standard model. From the above formula, the following conclusions can be inferred (the second follows from the first): 1. Contributions to the relative error of c E,M caused by errors in intensities and emission yields of the other elements are proportional to their concentrations. 2. At high concentrations of the element E (close to 1), contributions to dc E,M / c E,M from dI E,M and dR E are suppressed by normalization and the contributions from the other elements are small because their concentrations are small. Hence, for materials consisting mostly of a single element, the relative error of that element will be small, irrespectively of the errors associated with intensities and the calibration constants. The assumption of the errors dI E,M and dI F,M being random and independent is crucial: frequently, a substantial part of the intensity variations comes from a variable sputtering rate of the matrix. In such case, dI E,M and dI F,M are highly correlated, a substantial cancellation of the errors occurs and Eq. (29) significantly overestimates the actual error. The formula above is useful for practical applications. However, for testing the validity of the standard model, it is necessary to consider the deviations between the certified concentrations and the concentrations as predicted from the experimental data. Normalization, as described in Paragraph 3.1, would mix up prospective deviations associated with different elements and impair our ability to identify the matrix effects. Therefore, such tests are usually made so that the calibration, as described in Paragraph 3.2, is checked for selfconsistency. With a reasonably good instrument and using typical certified reference materials, it is usually impossible to achieve full self-consistency within the standard model, i.e. a situation that all observed deviations can be attributed to the random uncertainties of the measurements. A typical accuracy of the standard model for metals and alloys at the medium and high concentrations for the dc-GD-OES in the constant voltage – constant current mode is about 1% relative and frequently the deviations are comparable with the estimated uncertainty of the certified concentrations [73,88]. To my knowledge, no systematic data have been published so far about accuracy in the rf-GD-OES. In the analysis of non-conductive matrices, accuracy is generally worse than for metals and alloys. Accuracy in the GD-OES analysis can be considerably improved by using several or many lines for a single element [73], because of partial cancellation of the weak matrix effects by averaging. 4. Conclusions The beginning of what became later the standard model of GD-OES goes back to 1984, when the emission yields were

131

introduced as mere calibration constants in the sputter ratecorrected calibrations. After the introduction of the dynamic pressure regulation of the discharge gas in the early nineties, allowing the constant voltage – constant current operation mode of the dc discharge, it became apparent that the standard model produces accurate calibrations in a very wide range of the analyzed materials. Until recently, however, the standard model was considered as a purely empirical scheme and only little attention was paid to its connection to the underlying physics. This situation is gradually changing and the standard model is becoming an important link between glow discharge theory and experiment. A strong impulse towards further development of the methods based on the standard model was the recent introduction of commercial CCD-based GD-OES spectrometers, covering continuous spectral ranges. Especially the multi-element calibration fitting and the decomposition of complex spectra proved to be very useful in interpretation of the data from the CCD instruments. This includes analytical aplications, as well as studies of various fundamental processes affecting the signal response. The standard model can be considered a self-consistent scheme. Therefore, with the improvement of analytical performance of the GD-OES instruments, it is likely that further weak matrix effects will be revealed that will need explanation. The standard model is a powerful tool to searching for such matrix effects and offers a formalism for their quantitative description. References [1] W. Grimm, Eine neue Glimmentladungslampe fu¨r die optische Emissionsspektralanalyse, Spectrochim. Acta Part B 23 (1968) 443 – 454. [2] M.J. Heintz, P.J. Galley, G.M. Hieftje, Emission features of a conventional radio frequency glow discharge source and a magnetically enhanced source, Spectrochim. Acta Part B 49 (1994) 745 – 759. [3] J.B. Ko, New designs of glow discharge lamps for the analysis of metals by atomic emission spectroscopy, Spectrochim. Acta Part B 39 (1984) 1405 – 1423. [4] M.R. Winchester, C. Lazik, R.K. Marcus, Characterization of a radio frequency glow discharge source, Spectrochim. Acta Part B 46 (1991) 483 – 499. [5] M.J. Heintz, G.M. Hieftje, Design and characterization of a planar magnetron radiofrequency glow discharge source for atomic emission spectrometry, Spectrochim. Acta Part B 50 (1995) 1109 – 1124. [6] J.A.C. Broekaert, T. Bricker, K.R. Brushwyler, G.M. Hieftje, Investigations of a jet-assisted glow discharge lamp for optical emission spectrometry, Spectrochim. Acta Part B 47 (1992) 131 – 142. [7] F. Leis, J.A.C. Broekaert, K. Laqua, Design and properties of a microwave boosted glow discharge lamp, Spectrochim. Acta Part B 42 (1987) 1169 – 1176. [8] F. Leis, E.B.M. Steers, Boosted glow discharges for atomic spectrometry —analytical and fundamental properties, Spectrochim. Acta Part B 49 (1994) 289 – 325. [9] J. Angeli, A. Bengtson, A. Bogaerts, V. Hoffmann, V.-D. Hodoroaba, E. Steers, Glow discharge optical emission spectrometry, moving towards reliable thin film analysis—a short review, J. Anal. At. Spectrom. 18 (2003) 670 – 679. [10] A. Bogaerts, R. Gijbels, Fundamental aspects and applications of glow discharge spectrometric techniques, Spectrochim. Acta Part B 53 (1998) 1 – 42. [11] M.R. Winchester, R. Payling, Radio-frequency glow discharge spectrometry: a critical review, Spectrochim. Acta Part B 59 (2004) 607 – 666.

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