Electrical measurements at radio frequency glow discharges for spectroscopy

Spectrochimica Acta Part B 62 (2007) 1085 – 1122 www.elsevier.com/locate/sab

Review

Electrical measurements at radio frequency glow discharges for spectroscopy L. Wilken, V. Hoffmann ⁎, K. Wetzig Leibniz Institute for Solid State and Materials Research Dresden P.O.Box 270116, D-01171 Dresden, Germany Received 3 April 2006; accepted 14 July 2007 Available online 21 July 2007

Abstract This paper presents a review of the electrical radio frequency measurement techniques used in glow discharge optical emission spectrometry (GD-OES). In the introduction we show that for accurate quantitative chemical measurements reproducible electrical measurements are necessary. In the main part we introduce the techniques to generate the radio frequency (RF) and to measure voltage, current and power of the RF discharges. The required bandwidth of a RF current probe is estimated. Directional couplers used for the power measurement are introduced and their properties and limits are discussed. An overview of the different numerical and electronic evaluation methods for the voltage, current and power signals is given. New electrical measurements at the start up of a RF discharge and of a microsecond pulsed RF discharge show the benefit of the glow discharge source with integrated voltage and current probes. We present the use of the evaluated parameters to describe the dependence of the sputtering rate and the optical emission on RF discharge voltage and current using the model of Boumans and Bengtson. We also discuss the techniques to measure thick insulating materials and thin insulating layers with RF-GD-OES. Especially the evaluation of discharge voltage and current is presented in detail. © 2007 Elsevier B.V. All rights reserved. Keywords: Radio frequency; RF; Glow discharge; Optical emission spectroscopy; Plasma equivalent circuit; Plasma; Bulk analysis; Voltage measurement; Current measurement; Power measurement; GD-OES; Directional coupler; Pulsed discharge; RF generator

Contents 1.

2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Uncertainty in quantitative GD-OES measurements dependent 1.3. Measurement of pressure . . . . . . . . . . . . . . . . . . . 1.4. Intensity of argon emission line . . . . . . . . . . . . . . . . 1.5. Direct current discharges . . . . . . . . . . . . . . . . . . . 1.6. Measurement of DC voltage and DC current . . . . . . . . . Radio frequency discharges . . . . . . . . . . . . . . . . . . . . . 2.1. Fundamentals of RF discharges . . . . . . . . . . . . . . . . 2.2. Plasma equivalent circuit . . . . . . . . . . . . . . . . . . . 2.2.1. Negative voltages at powered electrode . . . . . . . 2.2.2. Positive voltages at powered electrode . . . . . . . 2.2.3. Circuit values. . . . . . . . . . . . . . . . . . . . . 2.3. Fundamentals of sputtering insulating samples . . . . . . . . 2.4. RF glow discharge sources . . . . . . . . . . . . . . . . . . 2.5. RF generation . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1. Fixed frequency RF generator and matchbox . . . . 2.5.2. Free running RF generator . . . . . . . . . . . . . .

. . . . . . . . . . . . on voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⁎ Corresponding author. E-mail addresses: [email protected] (L. Wilken), [email protected] (V. Hoffmann). 0584-8547/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2007.07.003

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2.5.3. Harmonic distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4. Electromagnetic compatibility (EMC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. RF measurement technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1. Fundamentals of RF measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2. RF voltage measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3. RF current measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4. Characterization of the glow discharge source with integrated voltage and current probes . . . 2.6.5. RF power measurement with current and voltage probes and an electronic multiplier . . . . . 2.6.6. RF power measurement with directional coupler and a diode detector . . . . . . . . . . . . . 2.6.7. RF power measurement of the glow discharge with a directional coupler and a diode detector 2.7. RF measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1. Voltage, current and power at the start up of the RF discharge . . . . . . . . . . . . . . . . 2.7.2. Voltage, current and power measurement for pulsed discharges . . . . . . . . . . . . . . . . 2.7.3. Current–voltage characteristic of a RF discharge . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4. Evaluation of characteristic parameters to describe the sputtering and the optical emission . . 2.7.5. Discharge voltage and current at insulating samples . . . . . . . . . . . . . . . . . . . . . . 2.7.6. Determination of the coupling capacitance of the insulator by a zero measurement . . . . . . 2.7.7. Voltage and current measurement at insulating samples . . . . . . . . . . . . . . . . . . . . 3. RF-GD-OES measurements at conducting samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Sputtering rates dependence on voltage and current . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Dependence of intensities on voltage and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Transformation of the sputtering rates and intensities to a standard voltage and current . . . . . . . . 3.4. RF and DC measurements at electrical conditions that result in identical intensities . . . . . . . . . . 3.5. Measurements with RF-GD-OES at standard voltage and current . . . . . . . . . . . . . . . . . . . . 4. RF-GD-OES measurements at non-conducting samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Voltage and current dependence of sputtering rates and intensities sputtering insulating samples . . . . 4.2. Calibration measurements at insulating samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Measurement of thin insulating layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature Nomenclature. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A. Polynomial constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix B. Materials used in this paper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction The electrical properties of discharges have always been of interest in discharge physics. Electrical direct current (DC) measurements are easy to perform, and do not disturb the discharge. For DC glow discharges a lot of documented discharge properties are directly related to the discharge voltage and current [1–3]. DC discharges used for glow discharge optical emission spectrometry [4] (GD-OES) with the aim to measure the chemical composition of solid samples and layered materials [5], require voltage and current measurements for the regulation of the discharge to constant conditions. A radio frequency (RF) generator is required for the measurement of insulating materials or insulating layers. Reproducible electrical RF measurements are necessary to adjust the discharge to constant conditions or to correct the intensities and sputtering rates in order to determine the chemical composition of all samples with sufficient accuracy. Today in some commercial RF plasma reactors for etching or physical vapor deposition (PVD), voltage and current probes are used [6] to detect the endpoint of an etching process or a faulty reactor state. It was shown that the voltage and current signals are suitable to evaluate the ion current [6–8]. RF voltage

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and current measurements are useful to meet the future requirements in the reproducibility and reliability of deposition and etching processes [9]. As in analytical glow discharges, ionization and optical emission are also correlated with the electrical plasma parameters in other sources. For techniques such as inductively coupled plasmas (ICP), electrical plasma measurements could improve the results of the analytical measurements [10]. In this review an overview is given on the radio frequency techniques, especially the measuring techniques, and their use for the GD-OES. The models used to calculate the chemical composition from the intensity measurements are introduced and the necessity of accurate electrical measurements as a prerequisite for the calculation of accurate chemical compositions is shown. Further parameters like pressure and intensity of argon emission lines as an alternative for the electrical measurements are discussed. Some properties of DC discharges are presented. In the section “radio frequency” we introduce the established techniques to generate the high RF voltage and to measure voltage, current and power. We show new electrical measurements at the start up of a RF discharge and of a microsecond pulsed RF discharge. In the following section we compare the dependence of the sputtering rate and

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

the emission on voltage and current for RF and DC applying the models of Boumans [11] and Bengtson [5] and show the use of the characteristic parameters for quantitative measurements with RF-GD-OES at conducting and non-conducting samples. 1.1. Theory In 1968 Grimm presented a glow discharge source and measured the intensities of the emitted light with a spectrometer [12]. He measured different certified reference materials (CRM) and found a linear relationship between the concentration ci of the element i in the sample and the intensity Ii of the related emission line: I i ¼ gi c i þ bi ;

ð1Þ

gi and bi are calibration constants. For the analysis of a steel sample some steel alloys were used. This represents a typical matrix specific calibration. In this case, the chemical composition of the standard reference materials must be similar to the chemical composition of the sample to be analyzed. Note, because each element has several emission lines usually two indices are used for the intensity (e.g. Iij). Only one emission line for each element and thus only one index (Ii) is used in this paper. The analysis of different materials, or layers on substrates, like zinc layers on steel, requires a calibration for different matrices. Such a method is also useful when the samples to be analyzed contain elements in concentrations that are not available in the CRMs with the same matrix, but in other CRMs. Thus, a more advanced model for matrix independent quantification must be applied. In glow discharge spectroscopy the sputtering and the excitation of the sputtered material are independent processes to a first approximation. Different materials are characterized by different sputtering rates. Boumans found in 1972 that the sputtering rate SR has a linear dependence on voltage U and current I [11]. SR ðU ; IÞ ¼ CQ IðU  U0 Þ:

ð2Þ

Herein CQ is the material dependent sputtering rate constant and U0 is a threshold voltage. The sputtering rate is defined as the mass loss Δm per time of sputtering ts: SR ¼

Dm : ts

ð3Þ

Different methods are used to measure the sputtering rate [11,13,14]. Further investigations showed that the intensity of an emission line also depends on voltage and current. Bengtson published the following model [15,16], Ii ðU ; IÞ ¼ ki ci SR ðU ; IÞgi ðU ; IÞ;

ð4Þ

where ki is a constant. gi(U,I) is an emission line dependent function given by I AIi ða0i þ a1i U þ a2i U 2 þ a3i U 3 Þ gi ðU ; IÞ ¼ ; IðU  U0 Þ

ð5Þ

1087

where AIi is a line specific constant for the dependence on current I and a0i, a1i, a2i and a3i are constants describing the dependence on voltage. A small selection is given in Table 5 in the Appendix [5,17]. If all measurements are performed at constant voltage U and constant current I (e.g. at standard conditions for an anode, da = 4 mm: 700 V, 20 mA) Eq. (4) can be written in the simplified form Ii ¼ Ri SR ci þ bi :

ð6Þ

This relationship represents the well known model of the constant emission yield. Ri is called “emission yield”. It represents the intensity of light emitted at an element specific wavelength divided by the mass per time of this element introduced in the discharge by sputtering. This means that the emission yield is matrix independent at constant voltage and current but variable pressure. Disturbances like self-absorption [18,19], line interferences [20], different background emissions [21], changes of the emission due to gaseous elements in the sample like hydrogen [22,23], oxygen or nitrogen [24] are not considered. For certified reference materials the intensities of different emission lines Ii and the sputtering rates SR are measured and the intensities Ii are shown in dependence on the product of the sputtering rate and the concentration SRci. A linear regression is used to determine the constants Ri and bi in Eq. (6). For an analytical sample the intensity of all elements of interest is measured and SRci is calculated using Ri and bi. With the condition that the sum of the concentrations of all elements in the sample is equal one X ci ; ð7Þ 1¼ i

the sputtering rate is calculated by: SR ¼

X I i  bi Ri

i

:

ð8Þ

Hence, to get accurate results all elements in the samples with certain content must be measured and used for the evaluation of the sputtering rate. During the measurement with the glow discharge analyzer the sample is sputtered layer by layer and the intensities are measured continuously, e.g. with a sampling rate of 1 kS/s [25]. The intensities Ii = Ii(t) are time dependent as well as the sputtering rate SR = SR(t) and the concentrations ci = ci(t). Due to the nearly flat crater bottom it is possible to determine the actual depth z(t) at a specific time. The mass sputtered per second [5] is given by dm ¼ SR ðtÞdt ¼ Aa qðtÞdz

ð9Þ

where Aa ≌ π(da / 2)2 is the area of sputtering and da the diameter of the anode. ρ(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 integration [26] of the last equation: 1 zðtÞ ¼ Aa

Z

t 0

SR ðsÞ ds: qðsÞ

ð10Þ

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Usually the density as function of time is calculated based on the composition that is known at this stage. For metallic materials the best results are obtained by summing over the fractional volume of each element [27,28]. The time dependent concentration ci(t) and the time dependent depth z(t) are transformed to a concentration depth profile ci(z). For conducting samples the voltage U of the generator usually is kept constant. The current I depends on pressure p and is in the first approximation I ∼p2 for a given material [29]. At constant pressure and voltage the current changes at different materials too. If aluminum is sputtered the current is about twice of that sputtering steel. To get a constant current for all measurements the pressure is changed. In modern glow discharge analyzers this is done electronically by an active pressure control. During sputtering of a layered material the pressure is automatically adjusted in a way that the current stays constant. Hence, it is necessary to measure voltage and current during depth profiling. For matrix specific DC-GD-OES analysis RSD values for the calculated chemical composition of less than 1% are state of the art [30–35]. Such accuracies are also desired when samples with different matrices or layered materials are analyzed using multimatrix calibration. In this paper we show the requirements for the electrical measurements as basis for an accurate chemical analysis. We rewrite the model of the constant emission yield (Eq. (6)): SR c i ¼

I i  bi : Ri

ð11Þ

It is usually used in commercially available GD-OES analyzers in this form. The intensity is proportional to the product of sputtering rate and concentration. Hence, in many practical applications the background is negligibly small (bi → 0). 1.2. Uncertainty in quantitative GD-OES measurements dependent on voltage and current We estimate the influence of the voltage and current measurement on the calculated element concentrations and depth. In the first step we estimate the deviations of the intensities dependent on the deviations on voltage and current. Eq. (2) is inserted into Eq. (4): Ii ðU ; IÞ ¼ ki ci CQ I AIi ða0i þ a1i U þ a2i U 2 þ a3i U 3 Þ:

ð12Þ

Voltage and current deviations are defined by ΔU and ΔI, respectively. The resulting intensity changes are calculated by DIi ðU ; IÞ DI DU þ agi ðU Þ ; ¼ AIi Ii ðU ; IÞ I U

ð13Þ

emission line with a negligible small background (bi → 0) will result in a deviation of the product of sputtering rate and concentration according to Eq. (11): DðSR ci Þ DIi ¼ : SR c i Ii

For the nearly pure matrix material, in this case Al, Eq. (8) simplifies to SR = IAl / RAl and the deviation of the sputtering rate ΔSR / SR and the depth deviation Δz / z are given by DSR DIAl Dz : ¼ ¼ z SR IAl

ð16Þ

The concentrations are calculated by ci = Ii / (RiSR) and the relative deviation is given by Dci DIi DSR ¼  : ci Ii SR

ð17Þ

The deviation of the concentration becomes zero for the main element. For simplicity we assume a current deviation ΔI / I while ΔU / U = 0. According to Eq. (13), we get an intensity deviation and according to Eq. (16) a sputtering rate and depth deviation of Δz / z = ΔIi / Ii = AIiΔI / I. For an Al-line (396.1 nm, AIAl = 2.4) a current deviation of ΔI / I = 1% results in a depth deviation of Δz / z = 2.4%. For the alloying element Cr (267.7 nm) the constant is AICr = 1.7. A current deviation of ΔI / I = 1% (ΔU / U = 0) results in an intensity deviation of ΔICr / ICr = 1.7%. The deviation of the concentration is calculated using Eq. (17) to |ΔcCr / cCr| = |ΔICr / ICr − ΔSR / SR| = |ΔICr / ICr − ΔIAl / IAl| = |1.7% − 2.4%| = 0.7%. Now we consider a voltage deviation ΔU / U, while ΔI / I = 0. For a fixed voltage U = 700 V agi(700 V) is calculated (Eq. (14)) using the constants in Table 5. For the Al-line agAl(700 V) = 0.59. For ΔU / U = 1% the intensity, sputtering rate and depth deviation is Δz / z = ΔSR / SR = ΔIAl / IAl = 0.59%. The constant for the Cr-line is agi(700 V) = 0.7 and ΔICr / ICr = 0.70%. Eq. (17) is used to calculate |ΔcCr / cCr| = |0.70% − 0.59%| = 0.11%. For some more emission lines and for iron with a low content of an alloying element we present the deviations of the calculated depth and concentration caused by a current deviation of ΔI / I = 1% (ΔU / U = 0) and a voltage deviation ΔU / U = 1% (ΔI / I = 0) in Table 1. Roughly, the depth deviations are given by Table 1 Estimation of the deviations for the calculated depth and concentrations caused by deviations in the voltage and current measurement

λ

Matrix

AIi

agi

nm

where agi(U) is given by Aluminum

ða1i þ 2a2i U þ 3a3i U 2 ÞU agi ðU Þ ¼ : a0i þ a1i U þ a2i U 2 þ a3i U 3

ð15Þ

ð14Þ Iron

As an example we use a material with a low concentration of a single alloying element, like aluminum cAl = 99.9% with a chromium content of cCr = 0.1%. An intensity deviation at an

Al Cr Si Mn Fe Cr Cu Mn

396.1 267.7 288.2 327.4 372.0 267.7 327.4 327.4

2.4 1.7 2.1 2.1 1.75 1.7 2.05 2.1

0.59 0.70 0.7 0.91 0.87 0.70 0.52 0.91

ΔI / I = 1% ΔU / U = 0

ΔI / I = 0 ΔU / U = 1%

|Δz / z|

|Δci / ci|

|Δz / z|

|Δci / ci|

%

%

%

%

2.4

0 0.7 0.15 0.35 0 0.05 0.3 0.35

0.59

0 0.11 0.37 0.32 0 0.17 0.39 0.04

1.75

0.87

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

1089

Δz / z = A IiΔI / I ≈ 2ΔI / I and Δz / z = agiΔU / U ≈ 0.8ΔU / U. The deviations of the calculated concentrations are given by Δci / ci ≈ 0.5 · ΔI / I and Δci / ci ≈ 0.3 · ΔU / U. Due to the different, but similar dependencies of the emission yields on voltage and current these estimations are in principal also valid for other emission lines and matrices. For calibration purpose (Eq. (6)) the sputtering rate SR of the CRMs is also required. The Boumans formula (Eq. (2)) shows the dependence of the sputtering rate on voltage and current and thus, deviations in the voltage ΔU and current ΔI measurement result in a sputtering rate deviation ΔSR:

the current I is proportional to the pressure squared p2 [29] already small pressure deviations Δp / p = 1% will cause significant current deviations ΔI / I = 2% (p = 5 hPa). The current is in fact not directly related to the pressure but to the gas density. Due to the gas heating, which is dependent on the power and the thermal properties of the sample [40], the gas density is not proportional to the pressure. Hence even for an optimal pressure measurement setup, the pressure may be disturbed by several effects and may not represent the properties of the discharge with a sufficient accuracy [41,42].

DSR DI DU þ ¼ : I U  U0 SR

1.4. Intensity of argon emission line ð18Þ

To get a relative deviation for the sputtering rate of ΔSR / SR ≤ 1% a relative deviation of ΔI / I + ΔU / (U − U0) ≤ 1% is required. Conclusion: Accurate measurements with a glow discharge analyzer require reproducible voltage and current measurements. To compare sputtering rates between different glow discharge analyzers voltage and current measurement of both instruments must be calibrated. 1.3. Measurement of pressure In a glow discharge analyzer the pressure p is usually measured and it is thus self-evident to use it also as an additional parameter to describe the discharge. This is even more interesting in the RF mode, where the discharge current is in practice often not available. For the analysis of thin layers in the nm-range the constant pressure mode is sometimes preferred. Hence, also quantification models were developed that use the pressure as parameter for the discharge [36]. Here we want to discuss the properties of the pressure measurement. The first point to note is that in several publications [35,37,38] pressure values are presented (b100 Pa), which are not in the normal mode of operation for an analytical glow discharge. In the book of Payling et al. [4] the pressures given vary in the range between 4 Pa and 1500 Pa. One reason is that in some glow discharge systems, the pressure is measured in the vacuum line, where the pressure is much lower than in the discharge volume. Care must be taken in the interpretation of such absolute pressure values [39]. The heat conduction pressure gauges (Pirani gauges) often used depend not only on pressure but also on gas temperature. The signal may also be disturbed by deposition of sputtered material on the heating wire. Due to the low sensitivity in the range of interest these pressure gauges are not very accurate and not sufficient reproducible. The pressure deviations are larger than 10%. Because different instruments use different pressure measuring techniques, it is difficult to compare the results between different research groups. Some of these problems could be solved using capacitive pressure gauges that have measurement accuracies better than 1% and connect these directly to the vacuum chamber, where the pressure is similar to the discharge pressure. But, because

In a glow discharge analyzer, the intensity of argon emission lines is usually measured. Because these intensities are correlated to the discharge properties, it is also attractive to use these signals as parameters for the discharge properties, especially for RF [43] and for insulating materials [41,42,44]. Although the argon emission line is usable for such measurements, there are some disturbing influences. It has been shown that the reflectivity of the sample surface influences the intensity of all lines by an amount dependent on the wavelength [45]. For conducting samples such as aluminum, steel and zinc, the changes are usually less than 15%. For surfaces with a high reflectivity like mirrors or polished silicon the changes can be as large as 100%. The sputtering of transparent layers results in interference effects [46,47]. A simple model has been presented that describes the intensity changes. Its use requires the introduction of the wavelength dependent reflectivity of the sample that is usually unknown. It is also documented that gases such as hydrogen diffusing out of the sample and the source change the intensity of the argon emission lines [22,23]. These changes depend on the hydrogen concentration and on the discharge conditions. A model presented by Payling et al. [48] is useful to compensate the influence of hydrogen to a certain extent, but several limitations still exist. Here we conclude that the argon emission lines are disturbed by several effects, which limit their use as additional parameter for quantification for a multi-matrix calibration. However, the reproducibility of the argon emission lines might be sufficient for a single matrix calibration, e.g. at glasses with different thicknesses. 1.5. Direct current discharges The Grimm type glow discharge source normally used employs of a hollow anode [12,49] (see Fig. 1A) and a flat sample acting as cathode. The anode is a tube perpendicular to the flat sample surface with a typical diameter of da = 4 mm. All measurements reported in this paper were performed with this kind of source. The distance between the anode and the cathode is about 0.15 mm. The discharge gas is usually argon at a pressure of 1–20 hPa. The DC cathode voltages are in the range from − 500 to − 1500 V, the currents are between 5 mA and 50 mA and the related current densities are 40–400 mA/cm2. The current depends on the sample material. Due to the total coverage of the cathode by the discharge, the voltage increases

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small. But, with increasing time of use the conductivity of the deionized water increases, so the leak current is not any more negligibly small in comparison to the discharge current. Wilken et al. [13] measured at a voltage of 1000 V a leak current of 0.15 mA, which is less than 1% for a typical discharge current of 15 mA at a da = 4 mm source. This becomes more important for sources with smaller anode diameters (da ≤ 2 mm), where the currents are also smaller. In practice the changes due to the leak current and other changes like the transparency of the focusing lens are corrected by the measurement of drift samples. 2. Radio frequency discharges

Fig. 1. DC discharge, A: scheme of discharge, B: potential in the plasma at the path shown in A according to Ref. [51], C: reduced current I / p2 versus voltage U according to Ref. [29], D: reduced sputtering rate SR / I versus voltage U.

at increasing current, which is typical in the abnormal mode of glow discharges [12]. In a first approximation and in a small range the discharge voltage U is linearly dependent on the discharge current I U ¼ U0 þ IRd ;

ð19Þ

where U0 is the threshold voltage and Rd the resistance of the plasma [50]. The sputtered material is excited in the discharge. To compare different discharges with different electrode areas, voltages and pressures similarity laws are used [2]. In the Grimm type glow discharge source the reduced current I /p2 in dependence on voltage U is given in Fig. 1C [29] and the reduced sputtering rate SR /I is given in Fig. 1D. Bogaerts et al. modeled the discharge and presented the electrical potential distribution in the plasma [51]. According to their results we show the potential for the path from a over b to c (Fig. 1A) in Fig. 1B. The cathode fall is the voltage difference between voltage at the cathode (U= −1000 V) and the anode (U = 0 V). The positive plasma potential is visible as well as the slow decrease to zero from b to c. 1.6. Measurement of DC voltage and DC current The measurement of the DC current and DC voltage is state of the art. The high voltage is divided by a resistive voltage divider and measured with an analog to digital converter. The current is proportional to the voltage at a resistor between anode and ground. Often the cathode plate and/or a rear electrode are cooled by the circulation of deionized water. Usually, dependent on the technical realization, the leak current of water cooling is

There are many publications about radio frequency techniques. The relevant theory is presented in Ref. [52] and their application in glow discharge spectroscopy is shown in Refs. [53,54] and other papers cited therein. We use RF, written in capital letters, as abbreviation for “radio frequency” and DC for “direct current” to conform with the abbreviations used for glow discharge (GD), optical emission spectroscopy (OES) and mass spectrometry (MS). The abbreviation of the radio frequency powered glow discharge analyzer is RF-GD-OES. In this section the fundamentals of RF discharges (2.1), plasma equivalent circuits (2.2), of sputtering insulating samples (2.3) and special RF glow discharge sources (2.4) are introduced. The subsection RF generation (2.5) presents the different types of RF generators and its technical features. We discuss the harmonic distortion as quality measure and the electromagnetic compatibility. Another subsection (2.6) is related to the RF measurement techniques, especially for voltage, current and power. The next subsection (2.7) is about actual RF measurement and shows some applications of the measurement techniques and the use of electronic and numeric evaluation procedures. We show the start up of a RF discharge and a pulsed RF discharge and introduce the methods to determine all elements of a plasma equivalent circuit. At the end of this section (2.7.7) we present the models and procedures to measure the electrical parameters when sputtering thick insulating samples. 2.1. Fundamentals of RF discharges A RF generator with the voltage URF is connected with a capacitor to the powered electrode with the voltage UE and the common ground is connected to the anode (Fig. 2). The alternating voltage with amplitude UA and frequency f accelerates the free electrons in the argon gas. A plasma is excited. Because the electrons have a higher mobility in comparison to the ions, they are absorbed at the conducting surfaces. The ions remain at the top of the surfaces and build up a positively charged sheath. Thus, the discharge itself has a positive potential to the anode. Due to the capacitive coupling the electrons remain at the hot electrode and charge it up to the negative bias voltage UB. The resulting time dependent discharge voltage at the powered electrode for conducting samples is: up ðtÞ ¼ UE ðtÞ ¼ UB  UA sinðxtÞ;

ð20Þ

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Fig. 2. Scheme of RF voltage and current of the RF glow discharge.

with ω = 2πf. For negative voltages the current is also negative. This ion current is quite small. For positive voltages a high electron current is present. 2.2. Plasma equivalent circuit The electrical behavior of a DC discharge is described by a resistor. For the RF case the equivalent circuit is more complex. The equivalent circuit of Schneider [55] simplifies to that of Köhler et al. [56] (see Fig. 3), when the inductive component of the bulk plasma is negligibly small. For low pressure discharges (p ≪ 1 hPa) only Ck, Dk and Ca, Da are used as equivalent values of the sheaths [57]. Some authors have used the equivalent circuit in Fig. 3 to describe the electrical behavior of the discharge in the Grimm type source [58–60]. The measurements in Refs. [59,61,62] are suitable to determine the value of Rk. Wilken et al. evaluated all elements of the plasma equivalent circuit for conducting samples and confirmed its validity for the Grimm type RF glow discharge [40,63]. The equivalent circuit was used to simulate the waveforms in Fig. 2 by PSpice. The following circuit values were used Rk = 15.8 kΩ, Ck = 0.767 pF, Rb = 61.9 Ω, Ra = 331 Ω, Ca = 78.7 pF, UA = 564 V. It represents a RF discharge (da = 4 mm) at steel (NIST1763) at a pressure of p = 11.6 hPa. In RF discharges the bulk plasma oscillates between both electrodes [52]. The sheaths increase and decrease their thickness. When the electrode voltage attains their positive maximum the bulk plasma nearly touches the electrode and the sheath has a minimal thickness. At the same time the sheath at the other electrode has its maximal extension. In the next half cycle the bulk plasma moves to the other electrode and nearly touches it. The sheath thickness at the other electrode is maximal. In the external

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circuit the charges oscillate between the electrodes of the coupling capacitor Ckr. The current integrated for one cycle is zero. The RF discharge in a Grimm type source (Fig. 1) is due to the high pressure (1–20 hPa) and the high current density (40– 400 mA/cm2) characterized as a moderate pressure γ-discharge [52]. The powered electrode (cathode) has a fixed area of Ak = 12.56 mm2 that is much smaller than the surface area of the grounded electrode (anode). Due to the different electrode sizes a negative bias voltage is established at the powered electrode, which results in a negative voltage during most time of the cycle (∼80%) [56]. During the rest of the cycle the electrode voltage is positive. The plasma equivalent circuit (Fig. 3) uses electrical components. On one side the equivalent circuit could be used to describe the electrical behavior of a complex RF generation system including the RF discharge. On the other side it is possible to evaluate plasma physical properties like the ion density of the sheaths if the circuit values are known. The last requires a more detailed understanding of the physical meaning of the circuit's elements. At first we introduce the meaning of the different components in electronics. A resistor is an element that limits for a given voltage the current by elastic collisions of the free electrons with the fixed atoms. The resistance is dependent on material, temperature, area and length of the resistive material. A capacitor that is biased by a voltage is charged. The electrons are accumulated at one electrode and removed from the other. The capacitance of a vacuum capacitor is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. In RF case the (displacement) current has a phase shift of 90° to the voltage. A diode allows the electric current to flow in one direction but blocks it in the opposite direction. For the description of the RF discharge and the component values of the plasma equivalent circuit we consider the separate behavior for positive and negative voltages at the powered electrode. 2.2.1. Negative voltages at powered electrode When the electrode voltage is most negative at ωt / 2π = 0.235 (Fig. 2) the sheath at the powered electrode has its maximal thickness and the bulk plasma has a minimal distance to the

Fig. 3. Equivalent circuit and scheme of the discharge (K = (cathode) powered electrode, A = (anode) grounded electrode). (Fig. 1 in Ref. [64]; reprinted by permission of Applied Surface Science.)

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grounded electrode. The current in the external circuit is also negative. It is determined by the ion current through the sheath at the powered electrode. This ion current is a flow of ions (Ar+ and ions of the sputtered material e.g. Cu+) from the boundary between the sheath and the bulk plasma to the negatively biased electrode [65]. The ions that bombard the electrode and acquire an electron are neutralized. Atoms are ionized in the boundary sheath and the bulk plasma. The ions move toward the powered electrode and the electrons toward the grounded electrode, which absorbs the bombarding electrons. The ions that are accelerated in the electrical field at the powered electrode bombard the electrode and eject a number of electrons from the electrode surface. Due to the small secondary electron emission coefficient γ the electron current through the sheath is much smaller than the ion current. These electrons are accelerated in the sheath to high kinetic energies. They are an important source for the ionization of atoms in the boundary between the sheath and the bulk plasma [65]. The fast ions that are accelerated in the sheath are neutralized by symmetric charge exchange with atoms [66]. The created slow ions are accelerated again and might also be neutralized by catching an electron from an atom. A flow of fast ions and fast atoms toward the powered electrode is produced that bombard its surface and erode it. Computer modeling experiments indicate that the most sputtering is produced by Ar atom bombardment (about 70%). The contribution to the sputtering made by Ar+ ions was found to be less (about 18%). The rest is caused by the sputtering with eroded metal ions Me+ (Cu+, about 12%) [66]. In the plasma equivalent circuit (Fig. 3) the current Ik represents the flow of ions from the bulk plasma toward the powered electrode. The flow of ions Ik especially the velocity of the ion flow is limited by collisions with atoms. This is represented by a sheath resistance Rk. According Ohm's law the sheath voltage is given by Uk = RkIk. The number of positive charges in the sheath divided by the sheath voltage Uk is equal to the sheath capacitance Ck. For negative electrode voltages the flow of electrons through the sheath is small. The electrons that are created in the boundary between the bulk plasma and the sheath are accelerated toward the grounded electrode, which absorbs the bombarding electrons. It was shown [51] that for negative voltages at the powered electrode the plasma potential is small (about 1/10 of the value of Ua when the voltage at the powered electrode is positive). Due to the small sheath voltage Ua the current Ia through the resistance Ra and the displacement current through the capacitance Ca are also small. The free passage of the electrons from the bulk plasma to the electrode is represented by the conducting direction switched diode Da. The flow of electrons Ib through the bulk plasma is limited by inelastic collisions with atoms, which is represented by the resistance Rb. Note, that Ub = RbIb is the resulting voltage of the bulk plasma. 2.2.2. Positive voltages at powered electrode When the electrode voltage is most positive at ωt / 2π = 0.735 (Fig. 2) the bulk plasma has a minimal distance to the powered electrode. At the grounded electrode a positive sheath with a maximal thickness is present. Similar to the processes at the

powered electrode the ions that collide with the grounded electrode must acquire an electron. In the boundary between the sheath and the bulk plasma the atoms are ionized. The ions move toward the grounded electrode and the electrons move toward the powered electrode absorbing these electrons. The flow of ions Ia that are created in the boundary between bulk plasma and sheath at the grounded electrode is limited by inelastic collisions. This is represented by the resistance Ra. The accumulated positive charges and the sheath voltage Ua determine the sheath capacity Ca. The diode Dk that is switched in conducting direction characterizes the free passage of electrons from the bulk plasma to the powered electrode. Hence, Rk and Ck are short circuited. Rb represents the limitation of the electron current Ib through the bulk plasma by inelastic collisions. 2.2.3. Circuit values In the Grimm type source the capacitance Ck of the sheath at the powered electrode is in the range 0.12 pF to 1.5 pF [63]. Due to the known area of the sheath Ak and due to the known sheath voltage it is possible to evaluate the sheath thickness. It is in the range between 75 μm and 1100 μm. The mean free path of the ions is limited by collisions with atoms to about 10 μm [53]. Rk limits the ion current and is in the range between 8 kΩ and 200 kΩ [63]. The capacitance Ca of the sheath at the grounded electrode is in the range 10 pF to 400 pF. It is about 100 times the value of Ck. One reason for the larger capacitances is the expansion of the sheath at the grounded electrode. An estimated sheath expansion between 1 mm and 6 mm is used to calculate the sheath area. With the model of a parallel capacitor the sheath thickness is calculated. It is in the range 0.5 μm to 100 μm, which is about 10% of the sheath thickness at the powered electrode. Ra is between 100 Ω and 5000 Ω. It is about 1% of the resistance Rk of the sheath at the powered electrode. It might be that due to the smaller sheath thickness the numbers of collisions are reduced. Possibly, this unexpected difference also points to the limit of physical interpretation of the used simple equivalent circuit. It was also found that Ca ∼ 1 / Ra. The resistance of the bulk plasma Rb is between 30 Ω and 400 Ω, which is about 0.5% of the value of Rk. Due to the small resistance and voltage of the bulk plasma the power consumption of the bulk plasma is only a small part (3%) of the total power. Wilken et al. [63] also evaluated the influence of the pressure p on the circuit values of the plasma equivalent circuit. Due to the gas heating the reduced ion current Ik / p2 and the reduced sheath thickness dkp are not invariant. A model is presented that uses the plasma power P as an additional parameter to correct the reduced ion current (Ik / p2)cor such that (Ik / p2)cor becomes invariant and is proportional to Uk. The constant is in the first approximation 0.7 mA/(kV hPa2). The reduced voltage Ua p−0.5 versus the voltage Uk is in the first approximation invariant and pCa−0.5 versus Ua shows a linear behavior. The reduced voltage of the bulk plasma Ub /p is in the range 0.5 V/hPa to 2.5 V/hPa. 2.3. Fundamentals of sputtering insulating samples When sputtering insulating samples the electrode is electrically isolated from the discharge volume. The RF radiates

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through the insulating sample into the discharge volume. Because of the oscillating electrical field the free electrons are accelerated and excite a discharge. Due to the larger mobility of the electrons in comparison to the ions the electrons flow to the bordering electrodes. The remaining ions build up the sheaths. In contrast to a conducting electrode an insulating electrode cannot absorb electrons. Raizer et al. [52] took the similarity of the plasma potential for conducting and dielectric coated or insulating electrodes as indirect evidence for the electron attachment to dielectrics. Above this negatively charged dielectric surface a positively charged sheath is built up, in which the ions are accelerated toward the sample. Due to the interaction of the ions with the electrons attached at the insulating surface the ions are neutralized. In the boundary between the sheath at the powered electrode and the bulk plasma atoms are ionized. The freed electrons are accelerated toward the grounded electrode, which absorbs the electrons. In the following half cycle the electrons that are generated in the boundary between the bulk plasma and the sheath at the grounded electrode are accelerated toward the powered electrode. The electrons that bombard the insulating electrode are attached to the surface. Similar to conducting samples ions and fast atoms sputter the surface of insulating samples. In Section 2.7.5 and the succeeding sections we present the techniques to measure the discharge voltage and current when sputtering insulating samples. 2.4. RF glow discharge sources DC generators are not usable to sputter insulating layers like paintings or thick insulating materials like glass or ceramics. Chevrier and Passetemps developed a system using a RF generator and a Grimm type glow discharge to sputter insulating samples [67]. They contacted the insulating sample with a backside electrode (Fig. 4). Mitchell and Casper contacted the sample from the front side using a modified cathode plate [68]. Hence, this source corresponds from the principal point of view with the original Grimm type source usually used with a DC generator. Analytis used a front side electrode with a thin insulating layer [69]. Due to the large coupling capacitance to the samples the RF is coupled effectively into the discharge. Wilken et al. proposed to couple the RF from both sides, the front side and the backside (Fig. 4) into the insulating sample to

Fig. 4. Schematic diagram of a Grimm type glow discharge source sputtering an insulating sample with the cathode (front side electrode) and backside electrode.

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get defined electrical conditions for samples with different thicknesses, materials and sizes [70,71]. 2.5. RF generation Radio frequency glow discharge analyzers are used for the analysis of a whole spectrum of materials, from nanometer thick conducting layers to millimeter thick insulating materials. For thick insulating material, the voltage drop at the insulator increases with material thickness and decreases with the dielectric constant of the material. To sputter a thick insulating material (ds N 2 mm) with a low dielectric constant (silica glass, εr = 3.1), we estimated in Ref. [62] that the amplitude of the RF voltage (f = 3.37 MHz) at the electrode should exceed UE N 3500 V. To measure thin layers the RF generator voltage should stabilize very fast. To resolve a surface layer with a sheath thickness of 1 nm at a sputtering rate of 100 nm/s the voltage should be stabilized in less than 10 ms. It is important that the voltage waveform for the different types of samples is the same. It was found that different spectra of the supply voltage cause different spectra of the optical emission [72]. A discharge generated with a sinusoidal waveform of voltage with low harmonic distortion and a discharge generated with a sinusoidal waveform of voltage with high harmonic distortion have different intensities of the emission lines (e.g. Fe, 372 nm). To get a reproducible optical emission it is necessary to generate supply voltages with similar or identical waveforms. Hence, a sinusoidal supply voltage with small harmonic distortion is a good prerequisite to get reproducible optical emission. Today the excitation of discharges by RF is often based on the concept to transfer the maximum power from the RF generator to the discharge [52,73]. The basic condition is that the impedance of the glow discharge source with the supply cable and the discharge is equal (complex numbers) to the output impedance of the generating system [73]. For the used system this impedance 1 / (1 / Rk + jωCq) is mainly determined by the resistance of the discharge (5 kΩ b Rk b 100 kΩ) and the capacitance of the connecting cable Cc and the glow discharge source Cq. Note that the capacitance of a coaxial cable (50 Ω) with a length of 10 cm is Cc = 10 pF. The glow discharge source with integrated voltage and current probes has a capacitance of Cq ≌ 40 pF. 2.5.1. Fixed frequency RF generator and matchbox The output impedance of fixed frequency RF generators (e.g. f = 13.56 MHz) is usually 50 Ω. To transfer a maximum of the generated power to the discharge it is necessary to match the output impedance of the generator to the input impedance of the glow discharge GE, to the capacitance of the cable Tc1 and to the source capacitance Cq (Fig. 5). A typical matchbox configuration consists of a Pi-network with two variable high voltage capacitors Cm1, Cm2 and a high current inductor Lm. The two capacitors are adjusted in such a way that the reflected power Pr is minimal, which means a maximal transfer of power to the discharge. The matching network is a high quality resonant circuit. Already small changes of the discharge due to the change of the sputtered material can cause a detuning of the matchbox. Hence,

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Fig. 5. Scheme of a fixed frequency RF generator with Pi-matching network and glow discharge source.

not the maximum power is transferred to the discharge and the RF electrode voltage UE is reduced. For compensation the matchbox is retuned, but the movement of the tuning components and the stabilization of the resonant circuit are time consumptive (>> 10 ms). Marshall et al. developed a working mode where the matchbox is not adjusted during a depth profile measurement [14]. The tuning capacitors Cm1 and Cm2 are locked down. They measure the forward Pf and reflected power Pr and adjusted electronically the power of the RF generator in such a way that the discharge power P is constant during depth profiling. For a discharge power of P = 7.5 W the RF generator supplies a power of PRF = Pf − Pr = 15.1 W (Um = 1000 V). This working mode requires a more powerful RF generator that can withstand a larger amount of reflected power without overheating. The benefit is a reduced start up and stabilization time of the discharge. 2.5.2. Free running RF generator A free running RF generator is an oscillator, e.g. according to Meiβner. In contrast to the fixed frequency RF generators with matchbox, changes of the discharge impedance are adjusted by a change of the resonance frequency in real time. Because the input voltage is the only variable the free running generator is easy to use. Fig. 6 shows a simplified equivalent circuit of a free running RF generator. The parallel resonance circuit of Lr and Cr is powered by the triode TO [40,62]. The impedance of the glow discharge source including power transmission cable and discharge is parallel to Lr and Cr and determines its resonance frequency (3.37 MHz). Changes of the discharge current will cause only a small frequency shift of less than 1% because the current in the parallel resonance circuit and the cable exceeds the discharge current by orders of magnitude. The high internal resistance of the triode (11 kΩ) is good matched to the

resistance of the discharge (5 kΩ b Rk b 100 kΩ) and the internal losing components [52]. Between 30% and 50% of the DC power are transferred to the RF discharge. The amplitude of the RF voltage UE is proportional to the DC voltage UDC. Hence, a high voltage DC power supply (UDC ≤ 3500 V) enables the generation of a high RF electrode voltage of UE ≥ 3500 V, when sputtering insulating samples. The reproducibility of the RF voltage amplitude is similar to the reproducibility of the DC voltage. The start up time is as fast as the start up of the DC power supply. 2.5.3. Harmonic distortion In the ideal case the RF voltage at the discharge is sinusoidal, but often with discharge ripples or harmonics appearing [75]. The non-sinusoidal discharge current is a current with a high harmonic content. The harmonics of this current can excite resonance frequencies of the RF generator and the power cable [76,77]. The output impedance of RF generators or matching networks is for frequencies different to the fundamental not matched to the impedance of the power cable. In the extreme case the cable is open or short circuited and behaves like a cable resonator that amplifies some harmonics of the discharge current [78]. In the RF generator resonance frequencies caused by stray capacitances and stray inductances might also be excited by harmonics of the discharge currents. In the frequency domain the amplitudes of the harmonics are given by Uνω. U1ω is the first, U2ω is the second harmonic. The total harmonic distortion or ripple factor kE is a number that defines the quality of a sinusoidal voltage [79]. It is defined by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pl 2 Umx kE ¼ Pm¼2 : ð21Þ l 2 m¼1 Umx The total harmonic distortion can be measured with a spectrum analyzer (e.g. Rohde & Schwarz, FSL3) or a modern oscilloscope

Fig. 6. Simplified equivalent circuit of a free running RF generator, with cables, a filter and GD source. (Fig. 2 in Ref. [62]; reproduced by permission of the Royal Society of Chemistry.)

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with a Fast-Fourier-Transformation [40,62]. At resistive loads (Match, 50 Ω) fixed frequency RF generators usually supply a sinusoidal voltage with a total harmonic distortion kE b 1%. But with a discharge the ripple factor becomes worse. Marshall et al. [14] reported a harmonic distortion of up to 6%. Miller et al. proposed to isolate the discharge to the matchbox and the RF generator electrically using a filter [72]. The filter makes the amplitudes of the harmonics independent of the source and the matching network. This resonant filter (Chebychev-filter) has for the harmonics a low input and output impedance between line and ground. In the ideal case the harmonic currents generated by the RF generator cannot pass to the plasma chamber and the harmonic currents generated by the plasma cannot pass to the RF generator. In Wilken et al. [40,62] the power is transferred to the GD source with a coaxial cable (1 m, 50 Ω) (Fig. 6). The parallel resonance circuit in the RF generator is for frequencies above the fundamental like a short circuit. At the resonance frequencies of the short circuited power line the current is amplified and causes the disturbances of the current signal (Fig.7 without filter). The capacitance Cl in the filter (Fig. 6) shifts the resonance frequency of the short circuited power line to lower frequencies and the resistor Rl attenuates this resonance. The measured harmonic distortion of the excitation voltage with discharge is kE = 1% [40]. Note that the voltage is nearly ideal sinusoidal (compare Figs. 9 and 19). The discharge current in Fig. 7 (with filter) is free of oscillations. We like to emphasize that the filter also reduces the current in case of a short circuit. Of course it is possible to integrate the functions of the filter into the free running generator.

electrical circuits, like the current and voltage measurement. Thus, it is of advantage to build the RF generation system in such a way that the interferences to other electrical circuits in the instrument are negligibly small. This is similar to the demand that the electromagnetic radiation of the whole instrument must not exceed the limits given in the international standards (EN 50081, CISPER11). The emission in the frequency range 5 MHz to 30 MHz, outside the industrial, scientific and medical (ISM) frequency bands (6.780 ± 0.015, 13.560 ± 0.007, 27.120 ± 0.163, 40.680 ± 0.020,…MHz), measured in the power line (230 V∼) must not exceed 60 dB (μV) = 1 mV (EN 50081) and in the frequency range 30 MHz to 230 MHz the electrical field in a distance of 10 m must not exceed 30 dB (μV/m). It is possible to fulfill these norms using a free running generator. This is proven in industrial applications, like carrier gas hot extraction analyzers that use a high power (kilowatt range) RF generator at a frequency of about 18 MHz. Even for instruments that use one of the ISM frequency bands, where the limits in the EN 50081 are orders of magnitude higher, we should consider that for the harmonics caused by the non-sinusoidal current an emission at higher harmonics (54.24, 67.80, 81.36, 94.92 MHz) is present that must not exceed the values given above. If a DC generator is used in the glow discharge analyzer we should consider that during ignition or a short circuit in times of several hundred ns a high current will also cause radiation of radio frequency in a wide spectral range.

2.5.4. Electromagnetic compatibility (EMC) A part of the RF power is radiated into the instrument and the environment. It causes disturbances to instrument internal

2.6.1. Fundamentals of RF measurement The radio frequency (RF) range commonly used in discharges is 1 MHz to 100 MHz [52], the related wavelength range is 300 m to 3 m. Throughout the time of the ion current the impedance of the glow discharge is high (N10 kΩ). During the time of the electron current the discharge impedance is low (b 500 Ω). For the description of sputtering and excitation the ion current region, where the discharge impedance is high, is most important and the system electrically behaves like an open cable. Standing waves are present [78,80]. At the end of the transmission line the voltage U(l = 0) has a maximum and the current I(l = 0) a minimum. Inside the transmission line voltage and current vary with the position. In Fig. 8 λ is the wavelength. For an exact measurement the probes should be placed as close as possible to the discharge.

2.6. RF measurement technique

2.6.2. RF voltage measurement A modern digital oscilloscope measures a signal, shows the waveform and evaluates several characteristic signal parameters. The peak–peak (PkPk) value of a voltage U(t) is calculated by UPkPk ðU ðtÞÞ ¼ ½MAXðU ðtÞÞ  MINðU ðtÞÞ; Fig. 7. Current signal of the GD source with integrated voltage and current probes, with and without filter. (Fig. 3 in Ref. [62]; reproduced by permission of the Royal Society of Chemistry.)

ð22Þ

where MAX and MIN determine the maximum respectively minimum of the signal. The mean value for periodical signals is

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The glow discharge source with integrated voltage and current probes uses a capacitive voltage divider with a dividing factor of 1/2000. Due to the AC coupling the scaled signal UUs does not contain a bias signal. Therefore, it is possible to evaluate the amplitude directly as CRMS value of UUs: pffiffiffi UA ðUU s Þ ¼ 2UCRMS ðUU s ðtÞÞ: ð27Þ Wilken et al. developed a bias evaluation procedure based on a voltage and current measurement [40,62]. The bias voltage is defined as the negative value of the electrode voltage, UBw = − UUs(tZ) at the time of the zero transfer of the current, ip(tZ) = 0 from negative to positive, dip(t) / dt N 0 at t = tZ. The short form is: Fig. 8. Amplitude of voltage and current at an open lossless transmission line in dependence on the distance from the open end.

the cycle mean value (CMEAN), which is the mean value for one or several periods: Z 1 tp U ðtÞdt: ð23Þ UCMEAN ðU ðtÞÞ ¼ tp 0 Herein tp is the time of one or several periods. The root mean square (RMS) value for periodical signals is the cycle root mean square value (CRMS) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z 1 tp UCRMS ðU ðtÞÞ ¼ ðU ðtÞÞ2 dt: ð24Þ tp 0 Due to the high electrode voltage of 1000 V (amplitude) for conducting and up to 3500 V for thick insulating samples a voltage measurement at a glow discharge source requires a high voltage probe. The voltage division factor of resistive voltage dividers that realize a DC coupling is usually 1/100 or 1/1000. Although the RF voltage is sinusoidal for the measurement of the total harmonic distortion factor and to satisfy a constant phase difference to the current signal the voltage probe must have a sufficient bandwidth N100 MHz (e.g. Tektronix P6015/ P6133, Philips PM893/109, GE3121). The scaled voltage of a resistive voltage divider Ut is due to the DC coupling equal to the electrode voltage UE and for conducting samples equal to the discharge voltage up(t) = UE(t) = Ut(t). The bias voltage is evaluated as CMEAN value (Eq. (23)) UB ðUt Þ ¼ UCMEAN ðUt ðtÞÞ:

UBw ðUU s ; ip Þ ¼ UU s ðtZ Þ;   dip ðtÞ for all tZ with ip ðtZ Þi0 and N0 dt tYtZ

ð28Þ

It is possible to evaluate this zero crossing very accurate by the tangent at the positive slope of the current signal (Fig. 9). The electrode voltage for a probe that uses a capacitive voltage divider is evaluated by UE ðUU s ; ip Þ ¼ UU s þ UBw ðUU s ; ip Þ;

ð29Þ

which is for conducting samples identical to the discharge voltage up(t). Note that the bias voltage evaluation procedure is also usable for non-conducting samples, where the bias voltage is not directly measurable. In glow discharge analyzers the characteristic values of the discharge voltage should be available in real time with a time

ð25Þ

It is possible to evaluate the amplitude of the sinusoidal voltage by UA = 1 / 2UPkPk(Ut) (Eq. (22)), but the CRMS value has due to the integration procedure a better reproducibility qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðUt ðtÞÞ  UCMEAN ðUt ðtÞÞÞ: ð26Þ UA ðUt Þ ¼ 2ðUCRMS In the upper diagram of Fig. 9 we show the bias voltage UB(Ut) and the electrode voltage that is equal to the discharge voltage UE(t) = up(t) = Ut(t) of a resistive voltage divider.

Fig. 9. Upper diagram: voltage and displacement current compensated current waveforms of a GD source with integrated voltage and current probes. Lower diagram: calculated power waveform (steel, p ∼ 10 hPa). (Fig. 7 in Ref. [62]; reproduced by permission of the Royal Society of Chemistry.)

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Fig. 10. Simplified electronic circuit with signals proportional to the bias voltage UB, to the positive peak voltage UA and the mean square of the input voltage ∼ 2U2A.

resolution better than 1 ms and without the use of an expensive oscilloscope. Thus, the evaluation is performed with electronic circuits [79]. Fig. 10 shows a simplified form. For the determination of the bias voltage UB a resistive voltage divider is required [81]. The mean value is evaluated by an integrator (Fig. 10) and measured by a DC voltmeter. Using a capacitive voltage divider the positive maximum of the voltage is similar to the amplitude UA, which is measured with a DC voltmeter. Hence, the diode in Fig. 10 (peak voltage) passes a current to the capacitor when its voltage is smaller than the divided voltage. The evaluation of the peak value is very sensitive to harmonic distortions. Marshall et al. [14] reported deviations due to the harmonic distortions of up to 15%. A procedure to correct this effect was mentioned but not presented in detail. With electronic circuits it is difficult to evaluate a signal for exact one or several periods, thus usually the root mean square (RMS) value of a voltage is evaluated. The signal of a thermocouple or an electronic multiplier and an integrator is proportional to the integrated square of the input voltage (Fig. 10 mean square voltage). An electronic multiplier can also evaluate the RMS value in real time with time constants of less than 10 μs. It is possible to develop a glow discharge source, where a resistive voltage divider is inserted. This allows the direct measurement of the bias voltage even with electronic circuits. However, this probe must measure voltages up to 3500 V and the superimposed bias voltage. Additionally, a bandwidth N 100 MHz is necessary to get near the working frequency a negligibly small phase difference between applied and measured voltage. For the measurement of insulating samples or insulating layers the bias voltage is not directly measurable, and up to now for the determination of the discharge voltage a digitizing system and a computer are necessary, so it is possible to use a capacitive voltage divider and the bias evaluation procedure for the bias measurement. 2.6.3. RF current measurement It is possible to calculate the RF current from the measurement of the voltage difference above a known impedance using a high voltage differential probe. Butler and Kino used this method and presented in 1963 current–voltage characteristics of a laboratory plasma chamber [82]. Due to the wide bandwidth power generator with an output impedance (e.g. 50 Ω) that is matched to the cable, the discharge current is free of disturbances (see Section 2.5.3).

An inductive current–voltage transformer is often used for the current measurement. The coil in Fig. 11 converts the current II into a secondary current that produces a voltage UI across the resistor Ras. The frequency dependent transfer function is given by UI ¼

Ras Ras II ; Ns þ jxN s AL

ð30Þ

where Ras is the value of the resistor, Ns is the number of turns of the secondary coil, and AL is the characteristic value of the ferrite core inside the coil [83]. For AL ≫ Ras / ωNs2 the transfer function (Eq. (30)) becomes frequency independent: UI ¼

Ras II : Ns

ð31Þ

The upper frequency is limited by the resonance frequency of the coil. Including the following amplification the effective transfer function of the current–voltage converter used is set to UI = 2 II V/A [40,62]. Which bandwidth is necessary to get a current signal that represents the discharge current? Wilken et al. found using the equipment in Ref. [62] (f = 3.37 MHz, bandwidth of current probe is 150 MHz, see Fig. 15) that the amplitude of the 30th harmonic was 1% of the fundamental and for the 60th it was 0.3%. Because the equivalent circuit including the circuit values was known [40] it was possible to simulate the influence of the bandwidth limitation of the current probe on the current waveform. For an ideal RC low pass filter the frequency fg or bandwidth at which the amplitude is 1 / √2 = 0.707 (−3 dB) of the maximum value is calculated by fg = 1 / 2πRC. An ideal current–voltage probe and a

Fig. 11. Scheme of a current–voltage transformer.

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Cn is determined by a zero measurement without discharge. The amplitude of the voltage Un and the current In are measured and Cn is calculated by Cn ¼

Fig. 12. Influence of a RC low pass filter with a bandwidth (−3 dB) to transfer 30 and 15 harmonics.

RC low pass filter were programmed in PSpice and the bandwidth was set in such a way that 15 or 30 harmonics were transferred. The resulting current waveforms are presented in Fig. 12. The higher the bandwidth of the filter the smaller is the difference to the simulation without filter. The current waveform for 30 harmonics is close to that without a low pass filter, while the current waveform for 15 harmonics shows more significant deviations. The spectrum (FFT) of the simulated waveform is similar to that in Ref. [62]. It is difficult to determine how many harmonics a current probe should transfer, to get an appropriate signal, but the transfer of 15 harmonics and thus a bandwidth of 50 MHz (working frequency 3.37 MHz) is in our opinion not sufficient. Current–voltage probes are commercially available (e.g., Person 2878/2877, Rhode & Schwarz ESH2-Z1/ESV-Z1, Solar 9323). These probes ensure a defined bandwidth and a good linearity [84]. Such probes have a shield between the primary coil, the inner conductor and the secondary coil to reduce the capacitive coupling into the secondary coil. The practical realization of the shield and the common ground determines the measurement accuracy [79]. As already discussed for an open cable the amplitude of the current depends on the position of the probe (Fig. 8). Most accurate measurements are possible, when the probe is placed as close as possible to the discharge. But, for each realization a small piece of cable will be left, which has a capacitance and will cause a displacement current that superposes the discharge current. For example a 1 cm coaxial cable with an impedance of 50 Ω has a capacitance of 1 pF. The displacement current id(t) is calculated by id ðtÞ ¼ Cn

duðtÞ ; dt

ð32Þ

where Cn is the stray capacitance and u(t) the electrode voltage. The discharge current ip(t) is calculated by ip ðtÞ ¼ iðtÞ  id ðtÞ:

ð33Þ

In : 2kfUn

ð34Þ

It is also possible to generate electronically a displacement current id(t) by an air tuneable capacitor connected with the power lead and common ground [61]. A second current probe is used to convert this current into a voltage. Both current signals are measured and subtracted with an oscilloscope. The measured current becomes zero by adjustment of the variable capacitor without plasma. Therese et al. use this set up for the current measurement at a Grimm type glow discharge source [61,85,86]. In the first approximation the current signal is similar to that in Fig. 9, but especially the electron current differs rather strong. In the ion current region oscillations or disturbances are visible [61,86]. Hargis et al. [84] presented a different technique to eliminate the displacement current at the point of the current measurement. They added a series circuit of an inductance and variable capacitance between the power input line and ground and adjusted the variable capacitance such that the displacement current at the point of current measurement is eliminated. The combination of the voltage divider and current transformer within one probe guarantees good mechanical stability and therefore a good stability of the phase difference. Such a probe can be inserted between the matchbox and the plasma source (Scientific Systems, Ireland and Advanced Energy Industry, USA, MKS). The bandwidth of these probes is less than 100 MHz. An electronic unit evaluates voltage, current and the phase difference for the fundamental and six harmonics. These probes are used at plasma reactors for deposition or etching processes. The numerical compensation suffers on the fact that the resolution of the measurement is determined by the current signal i(t). If an oscilloscope with a resolution of 8 Bit is used the resolution of the calculated discharge current ip(t) is smaller than 8 Bit. The resulting resolution depends on the amplitude of the displacement current id(t). If the displacement current is subtracted electronically, ip(t) can be measured with full resolution (e.g. 8 Bit). Anyway, a current measurement as close as possible to the discharge is advantageous. Hoffmann et al. [81,87] introduced a home made current probe into the power feed of a Grimm type glow discharge source. The simplified equivalent circuit is shown in Fig. 13 (left). Although the shield is optimally connected to the ground and the distance to the discharge is only about 3 cm the stray capacitance is Can ≈ 15 pF. This is mainly caused by the large stray capacitance of the water cooled backside electrode. Prässler compensated the displacement current numerically [59]. In the first approximation the current waveforms are similar to the calculated ones (Fig. 9). The current signal is also disturbed by the leak current of the water cooling (Rw in Fig. 13 left). Due to the capacitance Ce of the shielding of the current probe and the inductance LL a voltage in the mV range is generated that disturbs the current signal Ui [40].

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Fig. 13. Equivalent circuit of the voltage and current measurement, left: introduced into the power feed, right: for the glow discharge circuit with integrated RF probes.

Wilken et al. developed a glow discharge source with an integrated current and voltage probe [88]. The toroidal coil of the current–voltage converter and the metal ring of the voltage divider is mounted between the cathode plate and the body of the GD source (Fig. 14), which ensures a high mechanical stability [40,88]. The distance to the discharge is about 3 cm which leads to a stray capacity of Cn = 3.3 pF. Because the current probe is mounted in the grounded line, the current signal UI and voltage signal UU have the same common ground (Fig. 13 right). The capacitance Ce to the shield and the resistance Rw of the water cooling will not disturb the current signal. Because of the metallic cathode plate the current measurement for conducting samples is independent of sample size and position. The connection of the cathode with the backside electrode ensures defined electrical conditions especially for the measurement of insulating samples. The electrical RF emission is minimized by the shielding cup. The voltage dividing factor is set to 1/2000 and the transfer function of the current probe is 2 V/A (Fig. 14). The displacement current is compensated numerically using Eqs. (32) and (33). By sputtering of insulating samples the resolution of the current measurement with an oscilloscope is still reduced by these small displacement currents [89]. 2.6.4. Characterization of the glow discharge source with integrated voltage and current probes Due to the sinusoidal output voltage of the RF generator used, only the fundamental of the voltage probe must be calibrated. Because high voltage high frequency reference voltage sources are not available, a high voltage reference probe

was used [62]. It is calibrated at signal voltages (e.g. 10 V) with a calibrated generator at the working frequency (e.g. 3.37 MHz). With the source internal probe the voltage supplied by the RF generator (e.g. 1000 V) is adjusted to that of the reference probe. It is assumed that the reference voltage has an amplitude independent transfer function. The current probe transfers several harmonics and has a wide bandwidth. Due to the small discharge current (100 mA) an ordinary calibrated sine wave generator is suitable for calibration purpose. For a simple check it is possible to connect anode and cathode plate with a 50 Ω resistor. A supplied voltage of 5 V results in a current of 100 mA and will give a current signal of 200 mV, if the transfer function is 2 V/A. For plasma reactors used for deposition or etching processes the frequency dependent transfer functions of the probes and the reactors are determined and used to evaluate the plasma voltage and plasma current [84,90–92]. In Ref. [40] a procedure for a network analyzer is presented, which determines the transfer functions of the voltage and current probe inside the glow discharge source including the disturbing stray capacitance and inductance. This procedure is based on a linear model in which the electrode voltage UE = B11UU + B12UI and the discharge current IE = B21UU + B22UI are linear combinations of the voltage signal UU and the current signal UI. The complex parameters B11, B12, B21 and B22 are the transfer functions. The measurements are performed in the frequency range of 1 to 200 MHz. The voltage dividing transfer function B11 has a low pass characteristic (Fig. 15) with a bandwidth of 90 MHz. At 3.37 MHz |B11| is 2140, which is used to calculate the electrode voltage [40].

Fig. 14. Scheme of the Grimm type glow discharge source with integrated current and voltage probe. (Fig. 1 in Ref. [62]; reproduced by permission of the Royal Society of Chemistry.)

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Fig. 15. Transfer functions of the glow discharge source with integrated voltage and current probe measured with a network analyzer.

The current transfer function B22 is up to 100 MHz independent of the frequency. The magnitude |B22| is in the range (0.47 ± 0.01) V/A and the phase changes ± 5°. With increasing frequency of up to 200 MHz |B22| decreases to 0.1 A/V, which is caused by a resonance frequency (N200 MHz). The bandwidth is 150 MHz [40]. The disturbing displacement current caused by the stray capacitance Cn is given by B21. Because of |UE / IE| = |B11| / |B21| we calculate |B21| = |B11| · 2πf · Cn using Cn = 3.1 pF. The good agreement between calculated |B11| · 2πf · Cn and measured curve in Fig. 15 up to 100 MHz shows that the used function is correct. The inductive disturbance of the voltage signal is given by B12. With a coupling inductance Ln it is calculated by |B12| = |B22| · 2πf · Ln. With Ln = 25 nH the calculated value |B22| · 2πf · Ln for |B12| is in a good agreement with the measured one (Fig. 15). Due to the small current and high voltage the disturbances of the voltage signal are negligible. At a frequency of 9.9 MHz a current of 5 mA would cause a voltage signal of UE = 6.5 mV which is 4–5 orders of magnitude smaller than the voltage signal of the fundamental. The phase of the voltage signal at the working frequency is φ(B11(3.37 MHz)) = − 2.9° and that of the current signal is φ(B22(3.37 MHz)) = − 1.7°. The phase difference is caused by the low pass characteristic of the voltage probe and the different delay times of the amplifier. The phase difference of − 1.2° is compensated numerically [40]. We estimate the error for the current measurement to ± 2% [40]. Because no high voltage reference generator is available the deviations of the voltage measurement are estimated to ± 5%. The electrical measurements showed that the reproducibility of the voltage and current measurement with a digital oscilloscope is better than 1%.

2.6.5. RF power measurement with current and voltage probes and an electronic multiplier The power waveform pt(t) is the product of discharge voltage and current pt ðtÞ ¼ up ðtÞip ðtÞ and the mean power is calculated by Z 1 tp P ¼ Pðpt Þ ¼ pt ðtÞdt; tp 0

ð35Þ

ð36Þ

where tp is the time for one or several periods. In Fig. 9 the time dependent power pt(t) is presented. Because a stray capacitance does not absorb power it is possible to calculate the power using the voltage signal u(t) and current signal i(t). In Refs. [40,62] the relative accuracy of the power measurement is estimated to 7%. It is possible to realize this operation with a wide bandwidth multiplier (Fig. 16) that can evaluate at least 30 harmonics and an integrator with a time resolution ≪1 ms [81]. Due to the small disturbances of the voltage and current signals the power signal UP is also slightly disturbed. The use of an electronic compensation circuit reduces errors caused by phase deviations and will further improve the power signal. We like to emphasize that this kind of power measurement is usable for free running generators as well as for a fixed frequency RF generator with a matchbox. 2.6.6. RF power measurement with directional coupler and a diode detector Directional couplers measure the forward Pf and the reflected Pr power. The dissipated power of the system is PRF ¼ Pf  Pr :

ð37Þ

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1101

Fig. 16. Simplified schema of power measurement based on multiplication and integration of the voltage and current signals of the GD source with integrated voltage and current probes excited by a free running RF generator.

In the frequency range of interest coaxial directional couplers with concentrated impedances are often used [93]. They are characterized by a wide bandwidth [94]. In Fig. 17 the coupler designed by Buschbeck is presented [95–97], see also [79,95,98]. The voltage divider has a signal uus(t) = kv uRF(t) (e.g. kv = 1/50) and the current–voltage transformer gives uis(t) = kc iRF(t) (e.g. kc = 1 V/A). uft(t) is the sum and urt(t) is the difference of both signals (Fig. 17): uft ðtÞ ¼ uus ðtÞ þ uis ðtÞ ¼ kv uRF ðtÞ þ kc iRF ðtÞ urt ðtÞ ¼ uus ðtÞ  uis ðtÞ ¼ kv uRF ðtÞ  kc iRF ðtÞ:

ð38Þ

The power is the mean value of the product of voltage uRF(t) and current iRF(t). We use Eqs. (35) and (36), insert Eq. (38) and modify this formula Z 1 tp PRF ¼ uRF ðtÞdiRF ðtÞdt tp 0 Z tp 1 ðkv uRF ðtÞ þ kc iRF ðtÞ þ kv uRF ðtÞ  kc iRF ðtÞÞ ¼ dðk 4kc kv tp 0 v uRF ðtÞ þ kc iRF ðtÞ  kv uRF ðtÞ þ kc iRF ðtÞÞdt Z tp 1 ðuft ðtÞ þ urt ðtÞÞðuft ðtÞ  urt ðtÞÞdt: ¼ 4kc kv tp 0 The result is equal to: Z tp   1 uft ðtÞ2  urt ðtÞ2 dt: PRF ¼ 4kc kv tp 0

ð39Þ

Provided that the bandwidth of the voltage and current probes in the directional coupler are sufficient, then it is possible to determine the power for non-sinusoidal excitation voltages and non-linear loads, if uft(t) and urt(t) are measured with an oscilloscope and the calculations in Eq. (39) are performed. In this case it is even possible to measure the discharge power when the coupler is installed between the matchbox and GD source. Hence, its use is similar to that of voltage and current

Fig.17. Simplified scheme of a directional coupler including a diode detector in the output of a RF generator.

probes. Due to non-deal properties of all probes a directional coupler delivers more accurate signals in comparison to voltage and current probes, if the load is matched (50 Ω). If loads with a high or low impedance are used, voltage and current probes deliver more accurate measurements than directional couplers [99]. Thus, it is best to use a directional coupler between RF generator and matchbox and a voltage and current probe between matchbox and glow discharge source. A sinusoidal voltage with the amplitude UA and a linear load (R, C, L) result in a sinusoidal current with a phase difference φ to the voltage. With a known source resistance Rs (e.g. 50 Ω) the current is IA = UA / Rs. Together with the condition kc / kv = Rs Eq. (39) simplifies to Z ðkv UA Þ2 tp  ðsinðxtÞ þ sinðxt þ uÞÞ2 PRF ¼ 4kc kv tp 0  ðsinðxtÞ  sinðxt þ uÞÞ2 dt ¼

UA2 cosðuÞ: 2Rs

In this equation two unknown parameters (UA, φ) are present. For these conditions only two parameters must be measured to determine the power PRF. Buschbeck showed [95–97] that a diode detector and a DC voltmeter are usable to evaluate and measure the amplitudes of the sinusoidal signal Uf = MAX(uft(t)) and Ur = MAX(urt(t)). Buschbeck derived the following formula, which is a modification of Eq. (39) for the power measurement: 1 PRF ¼ ðU 2  Ur2 Þ ¼ Pf  Pr : ð40Þ 4kc kv f In practice an electronic multiplier is used to deliver the signals Uf2, Ur2 and Pf, Pr, respectively. The measurement with a coaxial directional coupler and a diode detector requires a sinusoidal excitation voltage with a low harmonic content, a known and fixed output resistance of the RF generator and a linear load, in such a way that the current is also sinusoidal. These conditions are not correctly fulfilled between matchbox and glow discharge source due to the nonsinusoidal discharge current and the unknown output resistance of the matchbox. 2.6.7. RF power measurement of the glow discharge with a directional coupler and a diode detector The most accurate measurements of power using a directional coupler including a diode detector are possible between RF

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Fig. 18. Simplified scheme of a power measurement based on a directional coupler and a diode detector.

generator and matchbox (Fig. 18). Marshall et al. [14] optimized the RF generator to a low harmonic distortion (b 40 dBc). The output resistance of the generator is fixed and known (50 Ω). They showed that with plasma the harmonic distortion of the voltage at the output of the matchbox is about 6%. We assume that the harmonic distortion of the voltage at the position of the directional coupler is even less. But even for optimal electrical conditions the power measured by the directional coupler is not necessarily the power of the discharge, because the connecting cables and the matchbox consume power too. The matchbox power losses caused by heating are in the range between 10% and 60% [100,101]. These power losses are not only dependent on the matchbox type but also on the adjustment and the discharge conditions. Marshall et al. assumed that in the GD source the radiation is also a source of power losses [14]. It is possible to measure the power losses Pl as a function of the applied voltage by a zero measurement under vacuum without discharge [102,103]. If the disturbance of the coupler by harmonics is negligibly small, it is possible to use this function to correct the power measurement also when the discharge is on. This procedure is called “subtraction method” or “blind power subtraction”. Marshall et al. [14] use this subtraction method. Without a discharge they adjust the matchbox in such a way that the input reflection factor r ¼ Pr =Pf

ð41Þ

is minimal. They verified that the power losses without discharge are proportional to the square of the electrode voltage UE: Pl ðUE Þ ¼ Pf ðUE Þ  Pr ðUE Þ ¼ UE2 =Rl :

ð42Þ

Rl is a parallel resistance that describes the losses of the matchbox, the cable Tc1 and the GD source for matched conditions. Its value is evaluated to R l = 114 kΩ. At UE = 1000 V (amplitude) the power loss is Pl = 8.7 W [14]. To get stable electrical conditions during a depth profile measurement Marshall et al. “lock down” the matchbox, that means the capacitors Cm1, and Cm2 are not moved [14]. This mode causes a non-optimal matching, the input reflection factor r of the matchbox is not minimal and the losses of the cable TC2 are not negligibly small. In the RF technique such cable losses are described by linear transformations [78]. Marshall et al. used a loss factor kl that is determined by the measurement of several resistors with values different to 50 Ω. They use this factor kl to

calculate the corrected forward power Pfc and reflected power Prc at the input of the matchbox Pfc ¼ Pf dkl Prc ¼ Pr =kl :

ð43Þ

For a coaxial cable Tc2 (RG400, 50 Ω, length = 25 cm) at Pf = 32.3 W, Pr = 10.9 W the loss factor is kl = 0.968. Marshall et al. [14] use the subtraction method in the following form to calculate the discharge power: PðUE Þ ¼ Pfc ðUE Þ  Prc ðUE Þ  Pl ðUE Þ:

ð44Þ

Hence, to generate a voltage of Um = 1000 V = 1.224 UA and discharge power of P = 7.5 W the RF generator must supply a power of PRF = 15.1 W [14]. For this condition more than 50% of the supplied power is consumed by the matchbox, the cables and the GD source. The use of Eqs. (42) and (44) implies that in the first approximation the absorption and the radiation are only dependent on the electrode voltage. Power losses in the matchbox caused by the remaining content of harmonics are neglected. It is also assumed that the current at the directional coupler is sinusoidal with a negligible small harmonic content. Note that the power measurement is not compared with other systems that measure the discharge power without significant disturbances (see Section 2.6.5). Payling et al. presented another approach [104]. They developed an equivalent circuit of the whole electrical system. The matchbox, the cable to the GD source, the source and the discharge are included. They investigated especially the influence of the settings of the matchbox tuning capacitors on the power losses and found that small changes of the capacitor adjustments result in large changes of the power. Thus, the use of the capacitor settings as additional parameters will not improve the determination of the discharge power. We conclude that several technical improvements of the RF generator including the matchbox and the use of an advanced subtraction method improve significantly the power measurement with directional couplers that are used in commercially available glow discharge analyzers. 2.7. RF measurements 2.7.1. Voltage, current and power at the start up of the RF discharge For certain conditions and for a particular generation/ matching system Lazik and Marcus found that approximately

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

1103

Fig. 19. Discharge voltage of external high voltage probe (GE3121) and current signal of the source internal current probe, where the displacement current is compensated electronically, measured with an oscilloscope (LeCroy, LC584A, 2 GS/s, bandwidth limit: 200 MHz) sputtering a copper sample and using a free running RF generator (3.34 MHz, with filter) that is switched on after presputtering (p = 9 hPa), top: scaled voltage signal UUs, center: discharge voltage up =Ut, bottom: discharge current ip.

a time of 250 μs is required for the establishment of the steadystate bias voltage [105,106]. We measured the start up behavior at the Grimm type glow discharge with integrated voltage and current probes (Fig. 19), where the displacement current is compensated electronically, and a free running generator including filter is used. An external high voltage probe that uses a resistive voltage divider (GE3121, 1/100) and thus transfers a bias voltage is used and delivers the scaled signal Ut. A presputtering of several minutes is performed to reduce the disturbing effects of desorbed gases or water at the surfaces of the sample or anode. After presputtering the discharge is switched off for a few seconds. For the following start up the signals UU, UI and Ut are digitized with an oscilloscope (LC584A, 2GS/s, 100000 points) the bandwidth of which is limited to 200 MHz. The voltage Ut(t)= up(t) is shown in the left part of the central diagram of Fig. 19. After the ignition of the discharge the voltage shifts to negative values. The bias voltage UB (Ut) = UCMEAN(Ut) evaluated as CMEAN value is presented in Fig. 20. UB increases after the ignition of the discharge nearly exponentially to 346 Vat 50 μs. After about 25 μs the bias voltage increased to 90% of the final value which is ten times faster compared to the value published by Lazik and Markus [105,106]. This fast stabilization is most probably caused by the placement of the coupling capacitor Ct (Fig. 6) close to the glow discharge source. The scaled signal of the source internal capacitive voltage divider UUs is presented in the top diagram of Fig. 19. After the ignition of the discharge it shows a negative bias voltage that

comes to a negative maximum after 12 μs and increases afterwards. The CMEAN value of this signal UCMEAN(UUs(t)) (Eq. (23)) is like a negative pulse, which is caused by the band pass characteristic of the capacitive voltage divider with a lower frequency of about 100 kHz that transfers the building up of the discharge bias. Here, this negative shift is a disturbance. The corrected scaled voltage is given by UU k ðtÞ ¼ UU s ðtÞ  UCMEAN ðUU s ðtÞÞ:

ð45Þ

The bias voltage is evaluated with the bias evaluation procedure (Eq. (28)) for the corrected voltage signal UBw(UUk,ip) and

Fig. 20. Evaluated values, UB(Ut), UA(UUk), UBw(UUk,ip), UCMEAN(UUs), P(UUk,ip) and P / UA of the voltage UUs(t) and up(t) = Ut(t) and current ip(t) waveforms presented in Fig. 19.

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is shown in Fig. 20 too. Even the use of the digitized voltage UBw = −UUk(tZ) at the points ip(tZ) ≌ 0 without the use of an interpolation results in a bias voltage curve UBw(UUk,ip) that agrees very well with the measured bias voltage curve UB(Ut). Already 3 μs after the ignition of the discharge the bias evaluation procedure produces a stable voltage value. The amplitude UA(UUk) of the voltage is evaluated with Eq. (27) using the GD source internal voltage probe and the corrected voltage signal (Fig. 20). UA(UUk) decreases 7% after the discharge ignites. An electronic regulation circuit could reduce these changes. Due to the electronic displacement current compensation it is possible to calculate the discharge current ip(t) just by the current to voltage transfer function (2 V/A). In Fig. 19 we see the increase of the current ip(t) and the change of the current waveform in the first 4 μs after the discharge ignition. The power P = P(UUk,ip) (Eq. (36)) (Fig. 20) increases in 4 μs after the ignition to a maximum and stabilizes to a constant value after 25 μs. The effective current P / UA shows a similar behavior. We conclude that the glow discharge source with integrated voltage and current probes and an electronic compensation circuit for the displacement current delivers reliable signals even of the start up of a RF discharge. The result of the bias evaluation procedure agrees with the direct measured bias voltage. The discharge voltage and power are stabilized in times of about 25 μs. 2.7.2. Voltage, current and power measurement for pulsed discharges A pulsed discharge represents a DC or RF operation that is switched on and off. The DC or RF power supply is switched on for a time ton and switched off for toff. The switching frequency fs in the pulsed mode is fs ¼

1 : ton þ toff

ð46Þ

The duty cycle dC is the ratio between ton to the period time dC ¼

ton : ton þ toff

ð47Þ

The instantaneous power Pi = P(ton) is the power during the time when the plasma is on and the mean power Pm(ton + toff) is the power during one pulse cycle with the duration time (ton + toff). Both are connected by the duty cycle Pm(ton + toff) = dC P(ton). For a duty cycle of 100% (toff = 0) the instantaneous power is equal to the mean power. Due to the reduced mean power Pm in the pulsing mode the temperature at the sample surface is also reduced [74]. This allows the measurement of thermally sensitive materials like glass, polycarbonates or materials with a low melting point like lead or tin. Short microsecond pulses with high instantaneous powers increase the sputtering, excitation and the ionization. Time gated operation allows the separate measurement of the pre-peak or the after-peak with special analytical properties [107–109]. The use of pulsed RF-GD-OES for an accurate determination of the chemical composition requires besides the measurement

and regulation of the mean voltage and power also the regulation of the effective duty cycle and the regulation of the voltage and power to constant values during the time, when the discharge is on. For millisecond pulsed DC and RF discharges the amplitudes of the voltages and currents are similar to continuous discharges [110–112]. Lewis et al. [113] could not measure the bias voltage UB or the amplitude UA for a millisecond pulsed RF (13.56 MHz) discharge with a high voltage probe and an oscilloscope. Note, the Nyquist–Shannon sampling theorem requires for this condition a sampling rate N27.12 MS/s and for a sampling time of 10 ms at least 271.200 points. The use of an electronic evaluation circuit (Section 2.6.2) could reduce the sampling rate significantly (e.g. 100 kS/s). Nelis et al. [114] reported for a millisecond pulsed RF that the power measurement with a directional coupler delivers similar power values for continuous and pulsed mode, but for shorter pulse length they could not perform reliable power measurements due to a low pass characteristic of the directional coupler. For microsecond pulsed DC discharges electrode voltages of several kV with duration times ton of several (tens) μs are used [115–117]. After the start up of the discharge the current shows a pulse with an amplitude of several ampere with μs duration times. It follows a steady-state current for the rest of the ton time with amplitudes of several tens of mA. Due to the current peak at the start up the current probe must transfer several tens of MHz. Because of the steady-state current during the rest of the ton time it must also transfer lower frequencies, down to 1 / ton (Eq. (30)). We present a measurement at a microsecond pulsed RF discharge with a free running RF generator and a switching frequency of fp = 4 kHz (ton + toff = 250 μs). UU and UI of the GD source with integrated probes and Ut of a separate high voltage probe (GE3121) are digitized (LC584A, 200 MS/s, 100,000 points, 200 MHz bandwidth). For the conducting sample the electrode voltage is equal to the discharge voltage up(t) =UE(t) =Ut(t) (Fig. 21). Due to an electronic displacement current compensation the discharge current is ip(t) = 0.5 A/V UI(t). The values of UA(UUk), UB(Ut), P, P /UA are calculated using the time of one period. The on-time of the RF voltage is determined as time difference between the half values of maximum UA. ton = 60 μs gives a duty cycle (Eq. (47)) of dC(UA) = 24%. The signal generator controlling the free running generator was set to a duty cycle of 30%. After the restart of the RF generator the voltage UA (Fig. 21) needs a time of 10 μs to reach the maximum and further 12 μs to stabilize. Note the value of UA during the plateau is about 500 V and the peak at the beginning has a maximum value of 530 V. At the beginning the bias voltage UB is 8 μs delayed to the voltage UA, which is similar to the start up of the RF discharge (Fig. 20), which is also reported by Nelis et al. [114]. During the pulse the bias voltage UB increases continuously up to a voltage of 422 V at the end of the pulse. The power P increases within about 7 μs to a maximum value of 22 Wand decreases continuously during the pulse to a value of 17.5 W at the end of the pulse, which might be caused by a temperature increase of the discharge gas. Note that at constant pressure with increasing gas temperature the gas density, current

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want to evaluate more advanced characteristic values of the measured current and voltage waveforms. The sinusoidal discharge voltage with amplitude UA, bias voltage UB sputtering a conducting sample is given by Eq. (20). The current waveform is more complex. In Fig. 22 the transformation of the voltage up(t) and current ip(t) waveform into a current–voltage I(U)-characteristic is shown. The time vanishes and remains in the clockwise circulation of the I(U)characteristic. It was shown [40,63] that for the evaluation of characteristic parameters it is possible to separate the I(U)-characteristic in a negative ion current region and positive electron current region. This allows also separating the plasma equivalent circuit in one for the ion current region and one for the electron current region. Rk is calculated to Rk ¼

up ðxt ¼ 90-Þ : ip ðxt ¼ 90-Þ

ð48Þ

The capacitance Ck is determined by: Ck ¼ 

Fig. 21. Electrical measurements of a pulsed RF discharge at the glow discharge source with integrated probes generated with a free running RF generator (3.37 MHz) and the evaluation of characteristic parameters (copper sample, p = 9.0 hPa).

and power decrease [40,63,118]. The power P has a delay of about 4 μs to the voltage UA, which is also a start up property of the discharge. The instantaneous power is Pi = 16.0 W, while the mean power during the pulse cycle is Pm = 4.0 W. Hence, the resulting temperature increase of the sample surface in pulse mode is about 25% of that in the continuous mode. The effective current P / UA has a similar time dependent behavior as the power P. The mean value of P / UA during the pulse is about 38.5 mA, while the current maximum is 42 mA. After the pulse the effective current P / UA needs 20 μs until it vanishes, which might be caused by a slowly vanishing plasma. It can be concluded that a glow discharge source with integrated voltage and current probes with an electronic displacement current compensation is usable to measure the RF voltage and current for pulsed RF discharges. This allows the evaluation of the mean voltage and power, and of the effective duty cycle. 2.7.3. Current–voltage characteristic of a RF discharge The current–voltage characteristic of the discharge contains various information. The bias voltage, RMS voltage and the power are simple to evaluate with electronic circuits. Here, we

DIp : 2xUA

ð49Þ

For its evaluation two straight lines parallel to the middle line of Rk and tangential to the I(U) curve are plotted (Fig. 22). ΔIp is the distance between these two straight lines. The graphical evaluation is intuitive but not very accurate. We should have in mind that due to the oscilloscope sampling rates of up to 2 GS/s most information is not used. Wilken et al. developed a procedure based on a sinusoidal fit to the voltage and current waveforms [40,63] to evaluate Rk, Ck and Uk numerically. In Refs. [40,63] a procedure to evaluate the elements Ra, Ca and Rb of the anodic part of the current is presented. By a method similar to the one above the voltage Ub and current Ib of the bulk plasma, the voltage Ua at the sheath at the grounded electrode (anode) and the effective current Ia through the resistance Ra are evaluated. We used the evaluated circuit values and calculated the current–voltage characteristic with PSpice [40,63]. Due to the good agreement between measurement and simulation (Fig. 23) we concluded that the description of the electrical system is sufficient. This is also confirmed by RF discharge modeling calculations, where the calculated voltage and current waveforms are in a good agreement with the measured ones [119]. The current waveform shows some deviations, but the principal behavior is correct. In contrast to the presented results in Ref. [137] it was shown that the discharge has a resistive character. 2.7.4. Evaluation of characteristic parameters to describe the sputtering and the optical emission In the introduction we showed that for the DC-GD-OES the voltage U and the current I are suitable to describe sputtering (Eq. (2)) and optical emission (Eq. (4)). Because the RF voltage and current are time dependent it is necessary to evaluate parameters from these waveforms that are suitable to describe sputtering and optical emission. In this subsection we introduce the different evaluations procedures and the evaluated parameters.

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Fig. 22. Transformation of up(t) and ip(t) to ip(up), bottom right: graphical evaluation of the elements Rk and Ck. (Fig. 2 in Ref. [63]; reprinted with kind permission of American Institute of Physics.)

The most simple and well known RF discharge parameter is the bias voltage UB (Section 2.6.2), which was suggested by Duckworth and Marcus [120]. The RF discharge behaves as a DC discharge at DC bias voltage superimposed by an alternating voltage. These measurements are performed at constant gas flow or pressure p. A directional coupler is usually integrated into a RF generator. So it is self-evident to use the power signal as an additional discharge parameter [121]. Note

that these RF systems are not optimized and the measured power is very different to the discharge power (Section 2.6.7). The measurements are performed at constant pressure p and generator power P. Payling [122] measured at constant bias voltage UB and power P and Bengtson [43] at constant URMS (Section 2.6.2) and P. Wilken [40] chose as parameter the ionic component of the voltage Uk, which is the mean value of the negative part of the

Fig. 23. Comparison of the measured and simulated (PSpice) (light gray lines) voltage and current waveforms (NIST1763, p = 11.6 hPa, Ueff = 400 V, Rk = 15.8 kΩ, Ck = 0.767 pF, Rb = 61.9 Ω, Ra = 331 Ω, Ca = 78.7 pF). (Fig. 6 in Ref. [63]; reprinted with kind permission of American Institute of Physics).

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voltage waveform up(t). It is calculated as integral of the negative values of up(t) between tk and tg, where up(t) is zero: Z tg 1 Uk ¼ up ðtÞdt: ð50Þ tg  tk tk

Here Cf is the capacitance of the insulating sample or the insulating layer. With a known dielectric constant εr and a known thickness ds of the insulator εd is given by

The ionic component of the current Ik is given by the current through resistive load Rk (Eq. (48)) of the sheath at the powered electrode:

With the area of coupling Ap the coupling capacitance of the sample is

Ik ¼

Uk : Rk

ð51Þ

It was shown that for electrical conducting samples [40,64] and a sinusoidal voltage the effective value of the negative voltage Uk is 1.5 times of the value of the effective discharge voltage UCRMS (Uk ≌ 1.5 UCRMS). The sheath at the powered electrode consumes 85% of the total power P (Pk = Uk Ik = 0.85P). The active current P / UCRMS is also proportional to Ik. Marshall et al. [14] used the fact that the time dependent voltage signal is almost completely negative biased and stated that the bias voltage UB is equal to the amplitude UA. They calculated the CRMS value of this voltage Um for the time of one period (tp = 2π / ω): ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 1 tp 2 ð1  sinðxtÞÞ dt ¼ 1:224UA : ð52Þ Um ¼ UA tp 0 This assumption is similar to the physical explanation that the argon ions are accelerated by a voltage difference between the positive plasma potential and the negative electrode voltage. The dependence of the voltage potential on the distance to the cathode in the DC case (see Fig. 1) and the time dependent voltage in the RF case (see Fig. 2) support this approach. Marshall et al. use additionally the advanced subtraction method to evaluate from the measured power the discharge power P (Section 2.6.7). They assume that the electrical power is completely consumed by the discharge and is used for the sputtering and excitation process. Analog to the foregoing discussion and due to the similarity to the DC case we define the effective current by: Im ¼

P : Um

ð53Þ

In the following Sections 3 and 4 we discuss the use of the evaluated parameters for the description of sputtering and optical emission. 2.7.5. Discharge voltage and current at insulating samples For insulating samples it is necessary to consider the voltage drop at the insulating sample in an adequate manner (Fig. 24). The discharge voltage up(t) is calculated by: Z 1 ip ðtÞdt: up ðtÞ ¼ uðtÞ  ð54Þ Cf

ed ¼

er : ds

ð55Þ

Cf ¼ e0 ed Ap ;

ð56Þ

where ε0 = 8.85 · 10− 12 F/m is the permittivity of free space. 2.7.6. Determination of the coupling capacitance of the insulator by a zero measurement Due to the existence of the cathode plate (Fig. 24) the glow discharge source with integrated voltage and current probes measures for conducting samples with different diameters, thicknesses and positions the same stray capacitance (Cn =3.3 pF) [40,62]. The backside electrode that is connected with the cathode plate is necessary to get defined and reproducible electrical fields in the insulating sample and the discharge. Both the cathode plate and the backside electrode are prerequisite for the function of the procedure that determines the coupling capacitance. For analytical samples the dielectric constant εr is usually unknown and the accurate determination of the insulator thickness ds is difficult. We found that the stray capacitance Cn is dependent on εd. Therefore, it is possible to determine εd = εd (Cn) by the measurement of Cn. Together with the area of coupling Ap the coupling capacitance Cf = Cf (Cn) is a function of Cn. Wilken et al. developed a procedure to determine the εd value of the sample by a zero measurement without discharge [123]. For conducting samples the electrical equivalent circuit is a parallel circuit of three capacities (Fig. 25). Cp represents the capacitance between the cathode (electrode) and the anode, Co the capacitance between the top of the anode and the conducting sample and Cg the capacitance between the anode and the sample without the region between the top of the anode and the cathode. The resulting stray capacitance Cn is calculated by Cn ¼ Cp þ Co þ Cg :

ð57Þ

The scheme of the Grimm type source sputtering insulating samples is presented in Fig. 24. The insulating sample is placed between the discharge and the backside electrode that is electrically connected with the cathode. The electrical equivalent circuit for insulating samples without a discharge is the right one in Fig. 25. Cp has the same value as for conducting samples. Due to the insulating sample, the two parallel capacities between the anode and the sample change to a series connection of Co and Ct parallel to a series connection of Cg and Cs. For insulating samples the stray capacitance is given by Cn ¼ Cp þ

1 Co

1 1 þ 1 : 1 þ Ct Cg þ C1s

ð58Þ

If εd of the insulating sample is known it is possible to calculate the capacities Ct and Cs, by the model of a parallel

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Fig. 24. Left: Scheme of Grimm type glow discharge source with insulating sample, right: equivalent circuit of the discharge and the coupling to the electrode. (Fig. 1 in Ref. [89]; reprinted with kind permission of Springer Science and Business Media.)

plate capacitor. With the outer diameter du and the inner diameter da of the anode (Fig. 24, left) Ct is given by "    # du 2 da 2 Ct ¼ e0 ed k  : ð59Þ 2 2 With the inner diameter of the cathode dq the capacitance Cs is Cs ¼ e0 ed k

 2 dq Ct : 2

ð60Þ

Eq. (57) is a simplified form of Eq. (58): For conducting samples the insulator thickness ds → 0, εd → ∞ (Eq. (55)), Ct, Cs → ∞ (Eqs. (59) and (60)) and Eq. (58) simplifies to Eq. (57). The remaining capacities Cp, Co, Cg are unknown. It is possible to determine the three unknown capacities (Cp, Co, Cg) in Eq. (58) by the measurement of the stray capacities Cnk of three different samples with known ratios of the dielectric constant to the layer thickness εdk. We propose to measure the stray capacitance Cn1 of one conducting sample and Cn2, Cn3 of insulating samples with different values of the dielectric constant to layer thickness (εd2, εd3). Eqs. (59) and (60) are used to calculate Ct2, Ct3 and Cs2, Cs3. The resulting system of equations is solved to Cp, Co, Cg. For the analytical sample Cn is measured and the εd value of the sample is determined using Eqs. (58), (59) and (60). The area of coupling Ap is necessary to calculate the coupling capacitance Cf (Eq. (56)). Wilken et al. found that due to a conducting plasma between the top of the anode and the sample the area of coupling is the area inside the ceramic Ap(dc) with the

diameter dc (Fig. 24) [89]. It is based on the observation that outside the crater the sample surface is changed, which is caused by a plasma where the energy of the ions is not sufficient to sputter the surface but sufficient to heat it up and modify it. Note that this plasma conducts the RF current. The use of the area Ap(dc) is also necessary to get an I(U)-characteristic that is describable by the plasma equivalent circuit. 2.7.7. Voltage and current measurement at insulating samples Wilken et al. used sintered aluminum oxide (Al2O3) as an ideal insulator. For the dielectric constant εr values between 7.1 and 8.5 are given in literature [138]. Due to the εr variation it is not possible to calculate an exact value of the coupling capacitance Cf for the 0.35 mm thick sample. A zero measurement gives Cn = 3.20 pF. εd (Cn) = 24.2 mm− 1 is evaluated and used to calculate Cf (Cn) = 5.8 pF, where Ap(dc) = 28.3 mm2. The electrical measurements of the sintered Al2O3 are shown in Fig. 26 Even though the stray capacitance of the glow discharge source with integrated current sensor is quite small (Cn = 3.20 pF), we see in Fig. 26 that the current signal i(t) is three times larger than the discharge current ip(t). Thus the resolution of the measurement for ip(t) is reduced. For thick insulating samples with a small dielectric constant, like 2 mm thick silica glass (εr = 3.7, Cf = 0.46 pF), the resolution of measurement would even be more reduced. The simulated (PSpice) I(U)-characteristic in Fig. 26 is in a good agreement with the measured one, which proves that the electrical behavior sputtering insulating samples is describable by the plasma equivalent circuit. Note the I(U)-characteristic in the electron current region is different to that sputtering a conducting sample. This means that also the discharge itself should be different. 3. RF-GD-OES measurements at conducting samples

Fig. 25. Equivalent circuit of the Grimm type glow discharge source for a zero measurement without discharge, left: for conducting samples, right: for insulating samples.

In this section we show the use of the evaluated electrical parameters (Section 2.7.4) (UB, UA, P, Uk, Ik, Um, Im) to describe sputtering and optical emission at conducting samples. RF-GD-OES measurements are performed at different voltages and currents and compared with DC-GD-OES measurements. The validity of the Boumans and Bengtson model for the RF-

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Fig. 26. Current voltage characteristic sputtering sintered aluminum oxide (Ap = 28.3 mm2, εd = 24.2 mm− 1, ds = 0.35 mm, Cn = 3.2 pF, Cf = 5.8 pF, Uk = 700 V, Rk = 58 kΩ, Ck = 0.3 pF, Rb = 1900 Ω, Ra = 100 kΩ, Ca = 3.4 pF, Ik = 12 mA). (Fig. 4 in Ref. [89]; reprinted with kind permission of Springer Science and Business Media.)

GD-OES measurements is proven. For fixed electrical conditions a direct comparison between DC- and RF-GD-OES measurements is shown. Finally we present quantitative RFGD-OES measurements at different certified reference materials performed at constant electrical conditions. 3.1. Sputtering rates dependence on voltage and current To show the dependence of the sputtering rate SR on voltage and current RF-GD-OES measurements at different voltages and current are performed, where usually the pressure is constant and the electrical parameters are measured. For RFGD-OES Payling et al. found a linear dependence of the sputtering rate SR on power P [121] and on voltage UB [122]. SR versus UA results also in a linear curve [43]. Bengtson et al. use the similarity of the sputtering rates between RF- and DCGD-OES measurements to adjust the RF power in such a way that the sputtering rates between RF and DC case become identical [43].

Wilken et al. [40,64] measured the sputtering rates of DC- and RF-GD-OES measurements that are performed for a wide range of voltages and currents. In Fig. 27 we present the reduced sputtering rates. We see that SR / Ik versus Uk results in a linear behavior. But the slope CQ of the fitted curve and the threshold value U0 between the RF and DC case are different. Thus, the chosen parameters Uk and Ik are not suitable to get a match of the sputtering rates between RF- and DC-GD-OES measurements. Marshall et al. [14] showed that the parameters Um and Im give reduced sputtering rates SR / Im nearly identical to reduced sputtering rates SR / I in the DC case. The slope CQ of the fitted curve and the threshold value U0 between RF and DC are in a good agreement. We recalculated the measurements presented in Fig. 27 from Uk and Ik to Um and Im and show the reduced sputtering rates SR / Im versus Um in the same diagram. For steel (NIST1761) the linear fits of the reduced sputtering rates for DC and RF are identical. The scattering of the single measurements to the linear fit is comparable for RF and DC. For aluminum (NBS1259) the slope CQ of the fitted curve is similar for the RF

Fig. 27. Reduced sputtering rates SR / Ik, SR / Im versus voltage Uk, Um for RF-GD-OES and SR / I versus U for DC-GD-OES for left: low alloy steel (NIST1761) and right: aluminum (NBS1259) (recalculation of measurements shown in Refs. [40,64]).

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and DC case but differs in detail, while the threshold values U0 are nearly identical. Note, that also Marshall et al. found such small differences in the slopes and threshold values of the fitted curves for different matrices between the DC and RF measurements [14]. We conclude that Um and Im are the parameters that give the best agreement of the sputtering rates between RF- and DC-GDOES measurements. 3.2. Dependence of intensities on voltage and current The model of Bengtson describes for DC-GD-OES measurements the dependence of the intensity as function of voltage and current versus sputtering rate and concentration (Eq. (4)). Due to the similarities between RF- and DC-GD-OES measurements the dependence of the intensities on voltage and current in RF-GD-OES should be similar to DC-GD-OES. Wilken showed [40] for RF-GD-OES measurements that the evaluated parameters Uk and Ik are suitable to correct the intensities Ii / gi(Uk,Ik) of a Cu- and Mn-line versus SRci in such a way that nearly a linear behavior results. In Fig. 28 we present another selection of these measurements [40] for a Fe-line sputtering steel (NIST1761) and an Al-line penetrating aluminum (NBS1259). We see that the RF measurements for Uk and Ik show a nearly linear behavior, but the slope and offset of this curve is smaller than that of the corrected intensities of the DC-GD-OES measurements. Hence, for the Al-line (396.152 nm) we used as parameter for AIAl instead of 2.4 the value 1.9. Marshall and co-workers showed that RF-GD-OES measurements performed at Um = U and Im = I give identical intensities to DC-GD-OES measurements. We assume that the parameters are also suitable to describe the dependence of the intensity on voltage and current. To show this we recalculate the measurements in Fig. 28 from Uk and Ik to Um and Im and show the corrected intensities Ii / gi(Um,Im) versus SRci in the same diagram. It is visible that the corrected intensities Ii / gi(Um,Im) are similar to the corrected intensities Ii / gi(U,I) in the DC case. For the measurements at the aluminum (NBS1259) the scattering of the single measurements to the fitted curve (10% or less) is caused by the use of an optimized value for AIAl = 1.9.

Here, we conclude that the parameters Um and Im describe the voltage and current dependent intensities better than the evaluated parameters Uk and Ik. Thus, we use for the following evaluations the parameters Um and Im. Bengtson et al. showed for DC-GD-OES that the corrected intensities are independent on the penetrated material [5,124,125]. The evaluated parameters Um and Im should also be usable to correct the intensities for different materials. For this purpose we use the measurements in Ref. [40] that are performed at different materials: aluminum (NBS1259), steel (NIST1761), brass (WSB1), zinc (CZ2009, CZ2012), ceramics (CC650) (see Table 6 in the Appendix). For an Al-line and a Mn-line we recalculate the measurements to Um and Im and present the sputtering rates and the intensities in Table 2. Each measurement is named by a small letter (“a”, “b”,…). The corrected intensities of the Al-line and the Mn-line show a linear behavior (Fig. 29). The deviations of the single measurements to the fitted curve are less than 10%. 3.3. Transformation of the sputtering rates and intensities to a standard voltage and current Up to now the best analytical results with DC-GD-OES are achieved for measurements performed at constant voltage and current. In commercially available glow discharge analyzers a computer controlled regulation is integrated to adjust the pressure in such a way that voltage and current are constant during a depth profile. But, there are also some applications, where a measurement at constant voltage and pressure gives better results, e.g. the measurement of very thin layers. For measurements at constant pressure p and constant RF voltage (amplitude UA or the bias voltage UB) [121,48], or at constant pressure p and RF power P [14,43,126] at different families of materials like steel, aluminum or brass the calibration curves show different slopes dependent on the type of material. This effect is called “family effect”. Different corrections for this artefact are presented in the literature [48,59,121]. The choice of a voltage different to the standard voltage is useful for some applications, e.g. to get a flat crater bottom and an improved depth resolution. Thus, in RF-GD-OES it is desired to measure

Fig. 28. Corrected intensities of a Fe-line (372.0 nm) sputtering steel (NIST1761) and an Al-line (396.1 nm) sputtering aluminum (NBS1259) by DC- and RF-GD-OES at different voltages U, Uk, Um and currents I, Ik, Im in dependence on SRcFe and SRcAl, respectively, left: IFe / gFe(U,I), IFe / gFe(Uk,Ik) and IFe/gFe(Um,Im) versus SRcFe, right: IAl / gAl(U,I), IAl / gAl(Uk,Ik) and IAl / gAl(Um,Im) versus SRcAl (U0 = 300 V).

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Table 2 Conditions of the measurements, Us =900 V, Is =25 mA, Al-line (396.1 nm), (AI =1.9 used instead of AI =2.4 a), gAl(Us,Is)=0.0338, Mn-line (403.449 nm), gMn(Us,Is)=0.0685 (concentrations are presented in Table 6) No.

CRM

Um

a b c d e f g h i j k l m n o p q

NBS1259 NBS1259 NBS1259 NBS1259 CZ2009 CZ2009 CZ2012 WSB1 WSB1 WSB1 CC650 CC650 NIST1761 NIST1761 NIST1761 NIST1761 NIST1761

a

Im

SR(Um,Im)

SR(Us,Is)

V

mA

ng/s

ng/s

1081 692 909 718 974 1098 1092 964 978 1106 829 710 1081 909 885 719 1094

39.5 34.3 27.1 23.6 27.6 29.5 33.5 32.7 24.6 26.2 32.9 28.0 39.1 24.6 37.3 24.2 31.3

4.20 1.91 2.41 1.44 18.89 23.70 13.30 15.27 12.65 16.10 0.58 0.30 9.50 5.21 6.82 3.40 8.03

2.04 2.13 2.19 2.18 15.24 15.09 7.51 10.54 11.39 11.46 0.50 0.39 4.67 5.23 4.70 5.04 4.85

IAl(Um,Im)

gAl(Um,Im)

IAl(Us,Is)

IMn(Um,Im)

gMn(Um,Im)

IMn(Um,Im)

3.965 2.618 2.025 1.460 0.794 0.906 2.327 0.412 0.247 0.270 0.369 0.209

0.0408 0.0613 0.0360 0.0419 0.7943 0.9060 0.0348 0.0397 0.0301 0.0274 0.0478 0.0495

1.597 1.614 1.730 1.795 0.645 0.633 1.280 0.243 0.250 0.237 0.225 0.186

0.043 0.033 0.026 0.023 0.187 0.209

0.0910 0.1233 0.0741 0.0791 0.0700 0.0647

0.022 0.024 0.024 0.027 0.147 0.141

0.071 0.051 0.054

0.0854 0.0613 0.0560

0.044 0.052 0.048

0.230 0.097 0.201 0.085 0.146

0.0901 0.0664 0.1081 0.0812 0.0693

0.086 0.101 0.088 0.106 0.087

See first paragraph of Section 3.2 for explanation.

at arbitrary voltages and currents. The transformation of the sputtering rates and the intensities to standard conditions represents the principle of the Bengtson model. For practical reasons we rewrite the Boumans formula (Eq. (2)) to transform the sputtering rate SR(U,I) from an arbitrary voltage U and current I to the sputtering rate SR(Us,Is) at a standard voltage Us and current Is: SR ðUs ; Is Þ ¼ SR ðU ; IÞ

Is Us  U0 : I U  U0

ð61Þ

The intensities are transformed from Ii(U,I) to the standard value Ii(Us,Is) using Eqs. (4) and (61): Ii ðUs ; Is Þ ¼ Ii ðU ; IÞ

Is ðUs  U0 Þ gi ðUs ; Is Þ : IðU  U0 Þ gi ðU ; IÞ

ð62Þ

The threshold voltage U0 is material dependent and for DC-GDOES it is in the range of 250 V b U0 b 350 V [13]. In the

following calculations we use a fixed value of U0 = 300 V, which is also proposed by Bengtson [5,125]. For the following evaluations we chose measurements within the range 700 V b Um b 1100 V, 15 mA b Im b 40 mA, which is sufficient to cover the current changes that will occur for measurements at constant pressure. In Fig. 30 we present the raw intensities of the measurements presented in Fig. 29 and Table 2 for an Al-line and the transformed sputtering rates (Eq. (61)) and intensities (Eq. (62)) to the standard conditions (Us = 900 V, Is = 25 mA). We see in Fig. 30 that the transformation moves each measurement to one linear curve. The deviations of the single measurement to the fit are less than 10%. In Fig. 31 we present for the Mn-line the transformation of the intensities and sputtering rates to the standard conditions. For the NBS1259 we subtracted the relatively high background intensity bMn before we used the transformation (Eq. (62)) and added bMn afterwards, with the result that the scattering of the single measurements to the fitted curve reduces significantly.

Fig. 29. Corrected intensities for an Al-line (396.1 nm) and a Mn-line (403.4 nm) sputtering different CRMs (Table 2) by RF-GD-OES at different voltages Um and currents Im in dependence on SRcAl and SRcMn, respectively, left: IAl / gAl(Um,Im) versus SRcAl, right: IMn / gMn(Um,Im) versus SRcMn (U0 = 300 V) (AI = 1.9 used instead of AI = 2.4 (see first paragraph of Section 3.2)).

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Fig. 30. Transformed sputtering rates and intensities of an Al-line (396.1 nm) from the measured conditions (Um,Im) to the standard conditions (Us = 900 V, Is = 25 mA) sputtering different CRMs (Table 2) (AI = 1.9 used instead of AI = 2.4 (see first paragraph of Section 3.2)).

For many measurements at standard conditions Us and Is, the calibration curves show small deviations. If the transformed curves for such a set of measurements are not disturbed by spectroscopic artefacts, like interferences and a high background intensity, and if enough measurements at different electrical conditions are available then it is possible to recalculate the constants (AIi, a0i, a1i, a2i, a3i) in such a way that the deviations of the single measurements to the calibration curve will be reduced. Here we conclude that the transformation of the sputtering rates and intensities from arbitrary voltages and currents to standard voltages and currents results in calibration curves with a small deviation of the single measurement from the fitted curve. To get better results for a measurement with high background intensity an adequate extension of the Bengtson model is required, if voltage and current are not kept constant. Note that the use of the Bengtson model requires the accurate voltage, current or power measurement for the whole range of

interest, which is here realized by the glow discharge source with integrated probes and an adequate signal evaluation. 3.4. RF and DC measurements at electrical conditions that result in identical intensities Marshall et al. [14] showed that RF measurements performed at Um = U and at constant RF power at P / Um = Im = I result in nearly identical intensities of RF- and DC-GD-OES measurements. We selected from a series of measurements, which are presented in Refs. [40,64] a DC- and RF-GD-OES measurement at aluminum (NBS1259), where the voltage and current nearly fulfill the condition Um = U, Im = I. The deviations of the RF and DC voltages and currents respectively are less than 2% (Table 3). The sputtering rates and intensities of the Al-line differ less than 5%. The pressures are identical. The deviations of the other emission lines are larger, which is caused by the small intensities. This was also found by Marshall et al. [14]. Wilken et al. choose another set of measurements [40,64] on steel, where the RF and DC voltage and current are similar but not identical (Table 4). To get a better match between both we transform the sputtering rate (Eq. (61)) and the intensities (Eq. (62)) of the RF measurements in such a way that the voltage and current are identical to the DC condition (Us = U, Is = I). The numerical values of gi(Um,Im) (Eq. (5)) and gi(Us,Is) in Table 5 are used. The differences between the DC and the transformed corrected RF measurements for the sputtering rates and for the intensities (Table 4) of the Fe-line are less than 2.5%. The differences of the other emission lines are larger. We confirmed that the RF voltage Um and the RF current Im are parameters usable to match the sputtering rates and the intensities of the RF-GD-OES to DC-GD-OES measurements, if Um = U, Im = I. 3.5. Measurements with RF-GD-OES at standard voltage and current

Fig. 31. Transformed intensities of a Mn-line (403.4 nm) and sputtering rates from the measured conditions (Um,Im) to the standard conditions (Us = 900 V, Is = 25 mA) sputtering different CRMs (Table 2).

For quantitative measurements of conducting layers like zinc on steel a multi-matrix calibration is required that includes different

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122 Table 3 Electrical conditions, sputtering rates and intensities of six emission lines, sputtering aluminum (NBS1259) for similar electrical conditions in DC and RF mode, where the values of the RF voltage and RF current are chosen to Um = U and Im = I

U/V I/mA p/hPa SR/(μg/s) IAl/a.U. (396.1 nm) ISi/a.U. (288.1 nm) ICu/a.U. (327.4 nm) IMn/a.U. (403.5 nm) INi/a.U. (341.5 nm) ICr/a.U. (425.4 nm)

DC

RF

1097 40.12 7.67 4.019 3.80 0.130 1.317 0.052 0.040 0.30

1081 39.51 7.64 4.201 3.97 0.131 1.245 0.044 0.056 0.27

types of CRMs like steel and zinc. For DC-GD-OES the best analytical results are obtained by sputtering the different materials at a standard voltage and current. Marshall et al. [14] received for RF-GD-OES linear calibration curves with a small scattering of the single measurement to the fitted curve, when sputtering all the different CRMs at constant voltage Um and at a constant power P. Wilken and co-workers performed measurements at constant Uk and Ik and received also linear calibration curves [40,64]. In Figs. 32 and 34 we present calibration curves for a Fe-,a Mn- and an Al-line [40] measured at Uk =700 V, Ik =12 mA penetrating different CRMs (steel, aluminum, brass, zinc, ceramic, see Table 6). Note the possibility to transform Uk and Ik to Um and Im. Here Uk = 700 V, Ik = 12 mA correspond to Um =803 V, Im = 11 mA. The constants Ri and bi in Eq. (6) are determined by a linear regression to the measurements in Fig. 32. The upper diagrams in Fig. 32 are not suited to see small deviations of the single measurements to the calibration curve. To get a better

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impression of the deviations we calculate the deviation RD of the intensities to the calibration curve:   Ii RD ¼  1 100: ð63Þ R i SR c i þ bi The deviations RD are shown in the lower diagrams of Fig. 32. For the Fe-line the deviations are in the range of 2%. The deviations of the Mn-line intensities to the calibration curve are due to the small intensities in the range of 5%. A more detailed study of the accuracy and precision of multimatrix quantification at GD-OES in DC mode was performed by Weiss at a significant amount of CRMs. Weiss [31] corrected the line intensities by the known spectroscopic artefacts, like line interferences, calculated the chemical composition of the reference materials and compared these with the given concentrations. The deviations dependent on the element, the concentration of the element in the sample are in the range between 0.1% and 10%. A practical guide for the error analysis for GD-OES measurements is given in Ref. [127]. 4. RF-GD-OES measurements at non-conducting samples In Section 3.3 we introduced Grimm type glow discharge sources that are usable to sputter insulating materials. Several measurements at insulating materials like glasses and ceramics are shown in Refs. [60,120,128]. Quantitative measurements of solid glass samples are presented in Refs. [41,42]. The authors used the intensity of an argon emission line to correct the changes of the emission line intensities due to the sample thickness. They found a linear dependence of the intensities on the sample thickness, which indicates that the discharge is very similar for insulating samples with a different thickness.

Table 4 Electrical conditions, sputtering rates and intensities of six emission lines, sputtering low alloy steel (NIST1761) for similar electrical conditions in DC and RF mode and RF sputtering rates and intensities that are so corrected that U = Um and I = Im

U/V I/mA SR/(μg/s) IFe(U,I)/a.U. (72.0 nm) gFe(U,I) ISi(U,I)/a.U. (288.1 nm) gSi(U,I) ICu(U,I)/a.U. (327.4 nm) gCu(U,I) IMn(U,I)/a.U. (403.5 nm) gMn(U,I) INi(U,I)/a.U. (341.5 nm) gNi(U,I) ICr(U,I)/a.U. (425.4 nm) gCr(U,I)

DC

RF

RF (calculated)

1190 16.55 5.240 1.048

1110 18.9 5.320 1.254 0.0149 0.056 0.0298 0.1008 0.0290 0.061 0.0389 0.506 0.0111 0.119 0.0558

1190 16.55 5.119 1.023 0.0126 0.037 0.0206 0.076 0.0228 0.045 0.0301 0.418 0.0095 0.084 0.0408

0.046 0.088 0.065 0.408 0.125

Fig. 32. Measurements at reference materials (brass: IARM82B, WSB1; steel: NIST1762, WIAM77, BSH8; zinc: CZ2014, CZ2010) sputtered at Uk = 700 V, Ik = 12 mA, top left: calibration curve for Fe (238.2 nm), bottom left: RD values for Fe, top right: calibration curve for Mn (403.5 nm), bottom right: RD values for Mn.

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Like for conducting samples it is also desired for insulating samples to use electrical measurements to control and adjust the discharge to constant conditions. It is necessary to consider the voltage drop at the thick insulating material in an adequate manner. In Section 2.7.5 we presented a model to calculate the discharge voltage up(t) from the electrode voltage u(t) and showed also a model (Section 2.7.6) that calculates the coupling capacitance Cf of the sample by a zero measurement without a discharge [89,123]. Note that the area of coupling Ap is set as the area inside the ceramic [40,89]. It is also found that the I(U)characteristic sputtering insulating samples is different to that sputtering conducting samples (Section 2.7.7). The use of the voltage and current measurements including the evaluation of characteristic parameters to describe the discharge sputtering insulating samples requires to test if the voltage and current dependent sputtering rates and intensities obey Boumans' respectively Bengtson's formulas. Furthermore the parameters should be feasible to adjust the discharge in such a way that for insulating samples with different thicknesses and compositions and for conducting samples linear calibration curves result. Finally we show a depth profile measurement at a thin insulating layer on a conducting material. 4.1. Voltage and current dependence of sputtering rates and intensities sputtering insulating samples Wilken et al. [40,89] measured the sputtering rate and the intensities sputtering a sintered Al2O3 sample (ds = 0.35 mm) at different voltages and pressures and they evaluated Uk and Ik. The reduced sputtering rate SR / Ik versus Uk results in a linear curve. Note that Boumans' law is satisfied. Because the parameters Um and Im give a good agreement between RF- and DC-GD-OES sputtering rates (Section 3.1) and intensities (Section 3.2) the measurements at the insulating samples are transformed from Uk and Ik to Um and Im (Uk = 700 V ⇒ Um = 1110 V, Ik = 12 mA ⇒ Im = 8.0 mA). The reduced sputtering rate SR / Im versus the voltage Um in the left diagram of Fig. 33 shows a linear behavior. The slope of the fitted curve is CQ = 0.020 ng/sVA, which is about 1/10 of that for aluminum (NBS1259, CQ = 0.149 ng/sVA, U0 = 330 V) (Fig. 27). The threshold value U0 = 600 V is nearly twice as measured for NBS1259. A physical explanation for this high threshold voltage of 600 V could not be found. In the right diagram of Fig. 33 we present the corrected intensities IAl / g(Uk,Ik) versus SRcAl for an aluminum line (396.152 nm, AIAl = 1.9) and see a linear behavior, which proves that the model of Bengtson is fulfilled. The sputtering rate and the intensity of the sapphire (thickness, ds = 0.55 mm) are identical with the sputtering rate and intensity of the sintered Al2O3 (thickness, ds = 0.35 mm), which proves that the measurements and the evaluations are not dependent on the insulator thickness. Here we can conclude that the electrical measurements at insulating samples and the evaluation of the parameters are usable to characterize the discharge sputtering insulating samples. The measurements show a similar behavior to those when penetrating conducting samples.

4.2. Calibration measurements at insulating samples At different conducting CRMs, sintered Al2O3 and sapphire at constant Uk and Ik (700 V, 12 mA) Wilken and co-workers measured the sputtering rates and the intensity of an Al-line [40,89]. The calibration diagram (Fig. 34) shows for the sintered Al2O3 and sapphire (IAl = 0.42) an intensity of 25% above the fitted curve of the conducting CRMs. It might be that the choice of the parameters Uk and Ik causes the increased intensity of the sintered Al2O3. The corresponding values Um and Im amount to Um = 1110 V, Im = 8.0 mA. For the conducting samples these values are Um = 803 V, Im = 11 mA. The transformation of the sputtering rate SR (1100 V, 8.0 mA) to SR (803 V, 11.0 mA) using Eq. (61) results in SRcAl = 11 ng/s. The intensity transformation (Eq. (62)) gives IAl (803 V, 11.0 mA) = 0.404 (Fig. 34), which is about 400% increased to the fitted curve. Thus, this simple correction does not result in an improvement. In Refs. [40,89] it is discussed that this emission yield increase might be caused by a different discharge to that penetrating conducting samples, which is indicated by the different I(U)-characteristic, and might be caused by the high oxygen content that could change the excitation processes. But with the new results, especially the linear behavior of the corrected intensity, we assume that the discharge sputtering of insulating samples is quite similar to the discharge sputtering of conducting samples. We believe that there is a problem at the correct scaling of the evaluated parameters. Note that one parameter is still adjustable, which is the area of coupling. For the calculation of the coupling capacitance we choose as area of the coupling the area inside the ceramics Ap = Ap(dc). This assumption is based on the observation that in the gap between the top of the anode and the insulating sample a plasma is present that conducts the RF current although it does not sputter the sample surface [40,89]. It might be that the plasma volume does not cover the whole area Ap(dc), but an area Ap(da) ≤ Ap ≤ Ap(dc). Other investigations showed that the size and influence of the plasma between the top of the anode and the sample depend on the pressure [63]. If for higher pressures the plasma in the gap between the top of the anode and the sample vanishes it should be possible to use the area of sputtering as area of coupling Ap = Ap(da). This will cause a change of the I(U)-characteristic that must still be describable by the plasma equivalent circuit, and a change of the evaluated parameters. Thus, it might be that the parameters Um and Im allow a sufficient matching of the discharge properties between insulating and conducting samples resulting in a better agreement of the emission yields. However, to answer these questions further investigations at a number of insulating materials with different thicknesses and compositions for several emission lines are necessary. 4.3. Measurement of thin insulating layers For paintings or polymer layers a concentration depth profile was calculated from the intensity–time profile using a single matrix calibration [129,130]. The authors determined for some

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

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Fig. 33. Sputtering rate and intensity (Al, 396.1 nm) of sintered Al2O3 (ds = 0.35 mm, Cf = 5.8 pF) and sapphire (ds = 0.55 mm, Cf = 4.9 pF), left: reduced sputtering rate SR / Im versus the voltage Um, right: corrected intensity IAl / g(Um,Im) versus SRcAl. (Left diagram Fig. 3 in Ref. [89]; reprinted with kind permission of Springer Science and Business Media.)

of the layers the chemical composition additional to GD-OES by further methods and used these layers as reference materials for the calibration of RF-GD-OES. Due to the similar structure and thickness of these samples the electrical conditions for the different samples are similar. An overview of such measurements is given in Ref. [131]. The use of a multi-matrix calibration for quantitative measurements of thin insulating layers is shown in Refs. [132,133]. These measurements were performed at constant voltage and power. Wilken et al. presented an intensity–time profile of anodized aluminum [40,89]. Due to the only 5 μm thick Al2O3 layer the coupling capacitance is about Cf ≈ 430 pF and the voltage drop above the insulating layer is negligibly small. The electrical measurements are evaluated in the same manner as for conducting samples. The pressure is manually regulated in such a way that voltage Uk and current Ik remain constant during depth profiling. In the top diagram of Fig. 35 it is visible that the time dependent voltage and current is constant (Uk = 700 V, Ik = 12 mA). For t N 3500 s the deviations are smaller than 1%. At the start of the measurement the current deviation is up to 40%, which is caused by the slow manual pressure regulation. The deviations at times of about 3400 s are also caused by the slow manual pressure regulation. In the central diagram of Fig. 35 the intensity–time profiles of the Al- and O-line show clearly the transition from the aluminum oxide layer to the base material aluminum. The discussion in Refs. [40,89] shows that the sputtering rate is 10–30% lower than that of sintered Al2O3 (3.9 g/cm3) due to the density in the range (2.7–3.5) g/cm3 [134]. Due to the comparable I(U)-characteristics [62] the electrical conditions sputtering the layer are identical to that sputtering conducting materials. Hence, the emission yield should also be identical. But, for the given sputtering rate the intensity is 35–55% increased in comparison to conducting samples. This is caused most probably by the high hydrogen content of the layer. Note that the porous Al2O3 layer of the electrochemical oxidation is usually densified by water vapor [134] to Böhmit (2 AlO (OH)). Thus, the layer contains up to 3% (mass) hydrogen. Such an amount of hydrogen causes an increase of the background

intensity [22,23,135] and for the Al-line (396.1 nm) an increase of the emission yield [43,136]. Due to the constant voltage and current the Ar-line (426.6 nm) has a constant intensity in the anodized layer and in the matrix material aluminum. This indicates that this emission line is not influenced by the hydrogen. In comparison to the anodized aluminum the increase of the Ar-line intensity in sintered Al2O3 is not clear. Due to the fast transfer from the oxide layer to the aluminum (Fig. 35) in times of 30 s the depth resolution is reasonable. For this 5 μm thick layer the estimated [40,89] relative depth resolution Δz / z is better than 10%. Here we conclude that the electrical signals of the glow discharge source with integrated probes are suited to adjust the discharge to constant voltage and current during the depth profiling of an insulating layer. The accurate quantitative measurement of anodized aluminum with RF-GD-OES requires

Fig. 34. RF-GD-OES measurements for an Al-line (396.1 nm) for conducting CRMs (a = NIST1762, b = BSH8, c = CC650, d = CZ2010, e = IARM87A, f = CZ2014) sputtered at Um = 803 V and Im = 11 mA, for sintered Al2O3 (ds = 0.35 mm, Cf = 5.8 pF) and for sapphire (ds = 0.55 mm, Cf = 4.9 pF) sputtered at Um = 1100 V and Im = 8 mA and estimated sputtering rate and emission of the sintered Al2O3 at Um = 803 V, Im = 11 mA.

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L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

Fig. 35. Top diagram: time dependent cathode voltage Uk and cathode current Ik sputtering anodized aluminum, central diagram: intensities of Al (396.1 nm), O (130.2 nm) and Ar2 (426.6 nm) sputtering anodized aluminum, sapphire, sintered Al2O3 and aluminum (HA-1), where the intensities of sapphire, sintered Al2O3 and aluminum are shown at arbitrary times, bottom diagram: crater profiles after 2000 s and 4000 s of sputtering. (Fig. 7 in Ref. [89]; reprinted with kind permission of Springer Science and Business Media.)

the determination of the layer density by adequate methods and the correction of the disturbances of the emission yields caused by the high hydrogen content of the layer. 5. Conclusions For quantitative measurements with glow discharge analyzers the measurement of the electrical parameters is important to achieve the required accuracies of the chemical composition and depth. We used the model of Bengtson and derived a formula to determine the depth and concentration deviations dependent on deviations on the voltage and current measurement. The depth deviation is given by Δz / z ≈ 2ΔI / I and Δz / z ≈ 0.8ΔU / U and the concentration deviation is Δci / ci ≈ 0.5ΔI / I and Δci / ci ≈ 0.3ΔU / U. Due to several disturbances the pressure is not a sufficiently reproducible discharge parameter. The intensity of argon emission lines is also disturbed. Hence, neither signal is suitable as a parameter to control the discharge for an accurate multi-matrix calibration. The fundamentals of RF discharges and a plasma equivalent circuit that describe the electrical behavior of a RF discharge are presented. We introduced two types of RF generators that are used to excite the discharge in the glow discharge source. The fixed frequency RF generator including the matchbox is improved by fixing the matchbox and producing an additional make up power to get a stable electrode voltage. The free running generator including a filter produces a voltage that has a

ripple factor of 1%. It is stabilized in times of less than 10 ms, which is necessary to analyze nm thin layers. This type of generator can also produce voltages sufficient to sputter thick insulating materials. We discussed some aspects of the electromagnetic compatibility. Also systems using the ISM frequencies radiate harmonics. For an EMV test these must be considered. Using adequate techniques it is possible to build a free running generator that emits less than the allowed limits in the EMV norms. Even DC generators can radiate electromagnetic waves that might exceed the limits in the EMV norms, when short circuits occur. We introduced numerical and electronic means to evaluate the cycle mean value, the cycle root mean square value and the peak value of a RF voltage signal and used these to determine the bias voltage and the amplitude of the discharge voltage. A detailed analysis of RF current measurement techniques showed that the measurement in the grounded line close to the discharge will supply the most accurate signals. To get a significant signal of the plasma current waveform the current probe should transfer more than 30 harmonics. This was tested by the measurement of the frequency dependent transfer function with a network analyzer. Due to the high electrode voltage the remaining stray capacitance of the current probe causes a nonnegligible small displacement current signal that is compensated numerically or electronically. Because of the accurate and good reproducible voltage and current signals the evaluation of the power with an electronic circuit in real time is also accurate and very reproducible.

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

The basics of the power measurement with a directional coupler and diode detectors were presented. The mathematical derivation showed that for an accurate measurement sinusoidal voltage and current waveforms are necessary as well as a fixed source resistance that exists at the output of a fixed frequency RF generator. The power losses of the matchbox, the cable and the GD source show a quadratic dependence on the electrode voltage and inverse one on the equivalent resistance. The cable losses from the RF generator to the matchbox must be considered in an adequate manner. A modified subtraction method that is dependent on the electrode voltage can be used to calculate the discharge power. To generate a plasma with constant voltage and power the electrical measurements are used to adjust the output power of the RF generator and the gas pressure. We presented here first time a voltage and current measurement of the start up of a RF discharge using the glow discharge source with integrated probes and an electronic displacement current compensation circuit. The evaluated bias voltage stabilizes in about 50 μs and the power stabilizes in about 25 μs. The bias evaluation procedure gives 3 μs after the ignition of the discharge reliable values that are in agreement with the measured bias voltage. Also for the first time, a voltage and current measurement of a microsecond pulsed RF discharge with a switching frequency of 4 kHz and a pulse length of 60 μs is shown. The evaluated amplitude of the voltage is stabilized in 10 μs after switching on, while after a fast increase to a maximum the power shows a slow decrease during the pulse, which might be caused by heating of the discharge gas. The measurement of the electrical parameters sputtering insulating samples requires the calculation of the discharge voltage. A model and a procedure were presented determining the coupling capacitance of the sample. The I(U)-characteristic of the discharge is different to that of conducting materials. The time dependent voltage and current signals provide new information about the discharge. We showed a simple procedure to evaluate the resistance Rk and the capacitance Ck in the ion current region. Together with the effective value of the negative voltage Uk the current Ik = Uk / Rk is calculated. Another useful parameter Um, that was introduced by Marshall et al., is the cycle root mean square value of the completely negative biased discharge voltage and the current Im = P / Um. The parameters Uk and Ik describe the dependence of the sputtering rates and the intensities on voltage and current. We recalculated our measurements from Uk and Ik to Um and Im and confirmed that the reduced sputtering rates and the corrected intensities of RF- and DC-GD-OES match well. We used Boumans' and Bengtson's model to transform the sputtering rates and intensities measured at arbitrary voltages and currents and different CRMs to standard voltages and currents and received a linear calibration curve with a small deviation (b 10%) of the single measurement to the fitted curve. Note that this model allows to quantify measurements that were performed at constant pressure and voltage or power. We also confirmed that DC- and RF-GD-OES measurements performed at U = Um and I = Im result in nearly identical sputtering rates and intensities — the intensity of the matrix element and the sputtering rate are within 2% in agreement. It

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was also shown that calibration measurements at constant voltage and current at different CRMs result in linear calibration curves that are similar to DC-GD-OES measurements. The dependence of the sputtering rate of insulating samples on voltage Um and current Im showed a linear behavior of the reduced sputtering rate on voltage, which proves the validity of Boumans' law. We could also show that the dependence of the intensity of an Al-line on voltage Um and current Im obeys Bengtson's law. Both tests indicate that the discharge sputtering an insulating sample is similar to the discharge with a conducting sample. Measurements at constant electrical conditions showed that the intensity sputtering a sintered Al2O3 is increased 25% to the intensity of conductive CRMs. The use of pulsed RF makes it possible to sputter insulating materials at usual GD pressures, which could reduce the plasma in the gap between the anode tube and the sample and thus allows using the area of sputtering as area of coupling. In any case, further investigations at different insulating materials (glasses, ceramics) with different compositions and thicknesses are necessary to find the reasons for the differences in the emission yield. It is possible to adjust the RF voltage and RF current during a depth profiling of anodized aluminum to constant conditions and get a constant intensity of an argon emission line. For quantitative measurements it is necessary to determine the density of the layer of the anodized aluminum with adequate methods and to correct the disturbances of the emission yields caused by the high hydrogen content of the layer. The improved voltage and current measurement technique allows the measurement of the discharge I(U)-characteristic, which can be used to evaluate all elements of the plasma equivalent circuit [62]. They are correlated with several physical discharge parameters, like the sheath thicknesses and the ion densities in the sheaths, the dimension of the bulk plasma, the electron density and electron temperature of the bulk plasma, the density and temperature of the discharge gas. For pulsed discharges the temperatures of gas and samples surface are of special interest. The additional discharge parameters can also be used to understand the changes of the discharge caused by light elements, like H, O and N and to improve thus the existing quantification models. Nomenclature List of symbols CMEAN Cycle MEAN value, it is the MEAN value for one or a few cycles CRMS Cycle Root Mean Square value, it is the RMS value for one or a few cycles CRM Certified Reference Material MAX Maximum MIN Minimum PkPk Peak–peak value RMS Root Mean Square value ε0 Permittivity of free space, ε0 = 8.85 · 10− 12 F/m εd Ratio of dielectric constant to thickness, εd = εr / ds εr Dielectric constant εdk εd of electrical calibration sample k

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Δci Δm ΔI ΔIp ΔSR ΔU Δz φ λ ρ ω a0i, a1i, agi Aa Ap AIi AL bi Bij ci Ca Cc Cf Cg Ck Cn Cnk Co Cp Cs Ct Cq CQ cAl da dc dC dk do dq du Da Dk f fs GE i(t) id(t) ip(t) iRF(t) I ICRMS Ik Ii

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

Uncertainty of the concentration of the element i Mass loss of the sample Uncertainty of DC current Difference current for determination of Ck Uncertainty of sputtering rate Uncertainty of DC voltage Uncertainty of the calculated depth Phase Wavelength Density Angular frequency, ω = 2πf a2i, a3i Coefficients of the voltage polynomial for the emission line I Constant dependent on voltage Area of sputtering, Aa ≌ π(da / 2)2 Area of coupling Current exponential coefficient for the emission line i Characteristic value of a ferrite core Background intensity Complex parameters of voltage and current transfer function Concentration of element i Capacitance of sheath at grounded electrode (anode) Capacitance of cable Capacitance of insulating sample Capacitance between anode and sample Capacitance of sheath at powered electrode (cathode) Measured stray capacitance Measured stray capacitance of sample k Capacitance between sample and anode (annular space) Capacitance between electrode and anode Capacitance of insulating material in series to Cg Capacitance of insulating material in series to Co Capacitance of glow discharge source Sputtering rate constant Concentration of aluminum Diameter of anode tube Inner diameter of ceramic tube Duty cycle Thickness of sheath at powered electrode Distance between anode tube and sample Inner diameter of powered electrode (cathode) Outer diameter of the anode tube Diode at the sheath at grounded electrode Diode at the sheath at powered electrode Frequency of RF generator, 3.37 MHz Switching frequency in pulsed mode Properties of the glow discharge including the conducting or insulating sample Time dependent current signal Time dependent displacement current Time dependent plasma current Time dependent current at the directional coupler DC current CRMS value of current signal for zero measurement Mean value of plasma current for negative values Intensity of element and line i

Intensity of aluminum line Measured current Effective discharge current, Im = P / Um Current at standard condition Current transfer of the directional coupler Calibration constant for element and line i Factor to correct the forward and reflected power Voltage transfer of the directional coupler Ripple factor of RF voltage with discharge Number of turns of secondary coil Pressure in discharge chamber Power consumption of discharge Forward power Instantaneous power in the pulsed mode Corrected forward power Power consumption of sheath at powered electrode Power loss Mean power in the pulsed mode Reflected power Corrected reflected power Power consumption of the system, PRR = Pf − Pr Reflection coefficient Resistance of sheath at grounded electrode (anode) Load resistance of current probe Resistance of bulk plasma Deviations of intensities to calibration curve Emission yield of line and element i Resistance of sheath at powered electrode (cathode) Loss resistance of matchbox and cable Output resistance of the fixed frequency RF generator Sample, MS/s = Mega sample per second Time Time when the discharge is on in pulsed mode Time when the discharge is off in pulsed mode Time for one or several periods Time of the zero passage of the current ip(t) Sputtering rate Time dependent voltage signal Time dependent voltage signal of forward power Time dependent voltage above the plasma Time dependent voltage signal of reflected power Time dependent voltage at the directional coupler DC voltage Voltage of the harmonic ν for the frequency ω Threshold voltage Amplitude of a sinusoidal voltage Bias voltage of a discharge evaluated by the CMEAN value of a signal UBw Bias voltage of a discharge evaluated with the bias evaluation procedure UCMEAN Cycle mean value of a voltage signal UCRMS CRMS value of voltage signal Uf Voltage signal of directional coupler, Pf ∼ |Uf|2 Uk Mean voltage above the sheath at the powered electrode Um CRMS value of the discharge voltage that is completely negative biased UPkPk Peak–peak value of a signal

IAl II Im Is kc ki kl kv kE Ns p P Pf Pi Pfc Pk Pl Pm Pr Prc PRF r Ra Ras Rb RD Ri Rk Rl Rs S t ton toff tp tZ SR u(t) uft(t) up(t) urt(t) uRF(t) U Uνω U0 UA UB

L. Wilken et al. / Spectrochimica Acta Part B 62 (2007) 1085–1122

Ur Ut UE UI URF Us UU UUk UUs z(t)

Voltage signal of directional coupler, Pr ∼ |Ur|2 Voltage of separate high voltage probe RF voltage at electrode RF voltage signal of current probe Voltage of a RF generator Standard or desired voltage for sputtering RF voltage signal of the GD source internal voltage probe Corrected and scaled voltage signal UU Scaled voltage signal Uu Time dependent crater depth

Acknowledgments

Appendix A. Polynomial constants Constants of the voltage and current dependent correction function gi(U,I) (Eq. (5)) that are used for the evaluation of the measurements in this paper. Table 5 Constants of the voltage and current dependent corrections [17]

Al Cr Cr Cu Fe Mn Ni Si

Current exponent

Voltage polynomial coefficients

λ/nm

AI

a0/V

a1

a2/V− 1

a3/V− 2

396.1 267.7 425.1 327.4 372.0 403.5 341.5 288.2

2.40 (1.90) 1.70 2.25 2.05 1.75 2.1 1.65 2.1

− 0.720 − 0.555 − 1.09 − 1.09 − 1.00 − 0.755 − 1.00 − 1.02

4.62E− 3 3.45E− 3 4.58E− 3 6.02E− 3 4.99E− 3 3.71E− 3 4.99E− 3 4.75E− 3

− 3.86E− 6 − 1.75E− 6 − 2.31E− 6 − 5.50E− 6 − 3.77E− 6 − 1.72E− 6 − 3.77E− 6 − 2.68E− 6

1.11E− 9 1.11E− 9 1.69E−9 1.05E−9 1.05E−9

Appendix B. Materials used in this paper Table 6 Concentrations and densities of the certified reference materials (CRM) Name

Material

ρ

Fe 3

NIST1761 Steel NIST1762 Steel BSH8 Cr–Ni CC650 Ceramics CZ2009 Zinc CZ2010 Zinc CZ2012 Zinc CZ2014 Zinc IARM82B Brass IARM87A Brass WSB1 Brass NBS1259 Aluminum Sapphire, ds = 0.55 mm Sintered Al2O3, ds = 0.35 mm

The concentrations are given in weight percent. NIST — National Institute of Standards and Technology, Gaithersburg, MD, USA; IARM — Analytical Reference Materials International, Evergreen, CO, USA; CZ — Czech Metrology Institute, Prague, Czech Republic; BSH8→BS — Brammer Standard Company, Inc., Houston, USA; NBS — National Bureau of Standards, Washington D.C., USA; WSB1→MBH — MBH Analytical UK. Concentration and density of CC650→Ceramic Alumina/TiC, Sandvik AB, Sweden, and the insulating materials Sapphire and Sintered Al2O3. References

This development was supported by the Spectruma Analytik GmbH. We are grateful to Prof. A. Bogaerts and Prof. E.B.M. Steers for constructive discussions at the preparation of this paper.

Element

1119

Al

O %

g/cm

%

%

7.79 7.81 8.19 4.28 6.59 7.13 5.35 6.98 8.5 8.31 7.81 2.76 3.99 3.9

95.085 94.093 14.61

0.055 0.069 0.18 36.5 5.07 0.172 20.1 0.967 0.002 0.42 1.9 89.78 52.9 52.9

0.107 0.286 0.027 0.023 0.083 0.92 0.1 0.205

Mn % 0.678 2.00 1.1

32.4 0.325 0.241 0.275 0.380 1.03 0.008 0.1 0.079 47.1 47.1

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