Optical spectroscopy for sputtering process characterization

Britun, Nikolay; Hnilica, Jaroslav

doi:10.1063/5.0006586

In this Tutorial, various methods of optical spectroscopy representing certain interest for magnetron discharge characterization are overviewed. The main principles, the implementation examples, and the selected results are given for each technique, accompanied by short discussions and suggestions for further reading. Both passive and active optical methods are covered, including optical absorption and laser-based techniques. The advantages and drawbacks of each diagnostic approach are critically analyzed. Special attention is devoted to the techniques extensively used by the authors in their own work, such as line ratio methods, absorption spectroscopy, interferometry, and laser-induced fluorescence.

I. INTRODUCTION

A. Characterization of sputtering processes

Sputtering is normally realized in low-temperature and low-pressure discharges. In order to study the properties of these discharges, spectroscopic diagnostics may often be required. The first record on sputtering is related to a glow discharge, when cathode sputtering has been observed, as reported by Grove in 1852.¹ About the same time, in the middle of the nineteenth century, the first ideas of using light emitted by glow discharges for their better understanding were discussed,² i.e., nearly two centuries after Newton’s discovery of prism and light dispersion (1666). Despite the pioneering role of cathode sputtering, in the recent six decades or so, the sputtering process is mainly associated with the so-called magnetron sputtering, where the magnetic field is formed above a cathode (target) by a set of permanent magnets. This results in efficient electron trapping above the cathode as well as in enhanced gas ionization and high sputtering efficiency.^3,4

Since the first ideas on magnetron sputtering proposed by Kay in the early 1960s,⁵ this technique went through several milestone changes and improvements, such as the introduction of pulsed sputtering,^2,6 radio-frequency (RF) sputtering² (actually known before the magnetron sputtering⁷), reactive sputtering,^8,9 high-power pulsed sputtering [also called high-power impulse magnetron sputtering (HiPIMS)],^10,11 including reactive¹² and bipolar HiPIMS^13–15 studied recently.

Efficient magnetron sputtering is a decisive technological solution for modern coating industry.^4,16,17 Because of this, sputtering processes require profound characterization for understanding their fundamental properties and physical behavior, which are important for further process improvement. Since the key point of any sputtering process is the transport of material from one surface (cathode) to another (film), correct determination of the fundamental plasma parameters, such as the mean energy and flux of the sputtered and reactive particles, their temperature, number density, velocity distribution, as well as the density and energy of the plasma electrons is of a great importance.

Some of the listed discharge parameters may also be crucial for discharge modeling as they may clarify key reactions related to plasma kinetics and plasma chemistry. The coexistence of modeling and experimental diagnostics has always played an important role in the understanding of sputtering. For example, early studies on energy distribution of the sputtered atoms (a fundamental characteristics of sputtering process) have been conducted both theoretically and experimentally. Theoretically, based on Sigmund’s model,¹⁸ it was concluded that the mean energy of sputtered neutrals might be estimated by the surface binding energy of cathode materials (typically several eV). Experimentally, this energy has been later measured using several optical methods, including the time-of-flight (TOF) technique, laser-induced fluorescence (LIF) as well as Doppler-shift interferometry showing reasonable agreement with theory.

The main subject of diagnostics is the study of fundamental discharge parameters. In the case of magnetron sputtering, diagnostics is a challenging task, as bulky or/and intrusive diagnostic tools, such as Langmuir¹⁹ and ion²⁰ probes, heat sensors,²¹ as well as mass spectrometer heads may often be affected by plasma (e.g., by the magnetic field in the case of Langmuir probes) or perturb plasma by themselves, thus affecting purity of experiment.

Regardless of the fact that non-intrusive methods may require additional data post-processing or/and signal calibration, the in situ non-intrusive discharge diagnostics is more favorable for precise and explicit discharge characterization as the latter remains unperturbed in this case. This work makes a special accent on spectroscopic discharge characterization techniques typically representing non-intrusive diagnostics. The basics, the implementation options as well as the operation advantages are discussed and critically analyzed along with the corresponding disadvantages for each diagnostic method.

B. Role of optical diagnostics

Optical diagnostic methods are traditionally subdivided into passive and active. The former ones utilize light spontaneously emitted by atoms and/or molecules normally excited by plasma electrons, whereas the latter ones rely on external light sources. Both groups have their advantages and drawbacks, and both were extensively used for magnetron discharge characterization during the previous decades.²²

A typical set for passive diagnostics may include an optical fiber connecting a vacuum chamber and a spectrometer/monochromator with a sensitive light detector, such as a photomultiplier tube (PMT) or a charge-coupled device (CCD) camera, whereas active diagnostics additionally requires external light sources, inducing coherent ones, such as laser. A generalized concept of a vacuum chamber with typical diagnostic tools is shown in Fig. 1(a). A cross-sectional view of a magnetron source with a flat laser beam used for laser imaging (see Sec. III B 4) is shown in Fig. 1(b).

FIG. 1.

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(a) Top view of a generalized magnetron sputtering reactor with the basic optical diagnostic tools, such as the monochromator, the intensified CCD (ICCD) camera, the spectral source for absorption spectroscopy, and a laser system. (b) Side view of a magnetron source indicating magnetic field lines, ionization zones, flat laser beams as well as the position of the spectral source beam (shown by dashed lines).

Numerous research works dealing with direct current magnetron sputtering (DCMS), pulsed DCMS, HiPIMS, and related discharges were conducted in the past having a goal to clarify the fundamental properties of magnetron sputtering by optical spectroscopy and related techniques.

Optical emission spectroscopy (OES) was one of the first techniques involved in diagnostics of the sputtering plasmas and has mainly been used for space- and time resolved discharge characterization, as a result of its straightforward implementation.^23–26 Two-dimensional discharge mapping has also been undertaken using OES imaging aiming at qualitative studies of the sputtered atoms.^27–29 More profound knowledge on the density evolution^23,30,31 as well as the velocity distribution^32–34 of sputtered atoms has been obtained soon afterward, involving laser-induced fluorescence.

Along with OES and LIF, the atomic absorption spectroscopy (AAS) technique has also been used for the number density and particle transport studies, mainly in the DCMS case. Hollow cathode lamps (Doppler broadening limited) and diode lasers (cavity finesse limited, i.e., normally much narrower) were mainly engaged in these studies.^25,31,35 Additionally, Fabry–Perot interferometry has also been employed^36,37 to determine the temperature as well as the velocity distribution of the sputtered atoms showing reasonable agreement with the early studies.

Pulsed sputtering discharges, in particular, HiPIMS, have also been widely investigated, namely, using OES,^38–42 emission line ratio methods,^40,43,44 OES imaging,^28,45–47 LIF,^48,49 LIF imaging,^15,50 AAS,^51–53 including tunable diode-laser absorption spectroscopy (TD-LAS)^54–56 as well as the other techniques. As a result, several fundamental phenomena in HiPIMS discharges were clarified: among them, the effects of plasma pulse duration on the ionization degree,^57,58 the transitional effects in the plasma emission at the beginning and at the end of plasma pulse,⁵⁹ as well as the effect of proportionality between the Ar line emission and the sputter yield.²⁸ Beside this, the effect of gas rarefaction at the end of the plasma pulse clearly affecting the width of the velocity distribution function (VDF) of sputtered atoms has been found at low Ar pressures using LIF spectroscopy.⁴⁹ It was shown that the VDF reveal the largest width at the end of the pulse, whereas the Ar atoms possess double-shaped VDF corresponding to thermal and non-thermal components.³⁹ Another example of using laser-based diagnostics is a clear separation of quasi-ballistic and diffusive transport of sputtered atoms in the HiPIMS achieved by TD-LAS.⁵⁴ Using the same method, the behavior of Ar metastable atoms (Ar $^{met}$ ⁠) has been clarified showing a clear density increase during the plasma pulse followed by its depletion at the end, primarily as a result of strong Ar ionization.⁵⁵

Recently, a necessity of understanding the time-resolved two-dimensional number density behavior of the ground state (GS) sputtered species during high-power pulsed sputtering has triggered the series of studies on the time-resolved GS density mapping in various discharge configurations, including unipolar^50,53,60,61 and bipolar¹⁵ cases. In these works, a detailed analysis of the number density evolution during the plasma-on and -off time is undertaken, including depletion effects, particle propagation, sublevel population inversion, etc. Some of these results are illustrated below.

Optical methods have also demonstrated their strength for detection of the self-organizing ionization zones in DCMS and HiPIMS discharges, often called spokes, rotating in the $E \times B$ direction above a magnetron target in the HiPIMS case as reported by Kozyrev et al.⁶² Spokes have been studied in the numerous works afterward, mainly involving OES imaging.^46,47 In addition to the planar view, a flare ejection from the spoke region in the azimuthal direction has been successfully visualized⁶³ using a streak camera, another emission-based diagnostic tool for ultrafast optical measurements.⁶⁴ Also, an attempt of direct visualization of the ground state ion distribution inside the spoke region has been performed by LIF imaging showing a certain correlation between the OES and LIF traces.⁶⁵ An in-depth discharge characterization by optical spectroscopy and the other methods has always been tightly related to the development of sputtering processes. This has resulted in the appearance of the new sputtering-based plasma processes, such as the multi-pulse⁶⁶ and bipolar¹⁵ HiPIMS discharges. These processes are still far from being understood fully requiring more intensive diagnostics work in the future.

The list of literature sources should not be limited by only the examples given above, primarily for the sake of illustration. There are numerous worth reading reviews related to the important aspects of plasma spectroscopy, including the spectroscopy basics overviewed by Fantz,⁶⁷ line ratio methods covered by Zhu and Pu,⁶⁸ as well as the fundamental review on plasma spectroscopy by Cooper.⁶⁹ For more curious readers, a set of the corresponding textbooks is also recommended, including the classical work on atomic spectroscopy by Mitchell and Zemansky,⁷⁰ the book covering the absorption and fluorescence basics by Kirkbright and Sargent,⁷¹ the one related to the various diagnostic aspects edited by Lochte-Holtgreven,⁷² and the one focused on low-temperature plasma spectroscopy by Ochkin.⁷³ The fundamental works of Griem, related to plasma spectroscopy basics⁷⁴ and line broadening,⁷⁵ are also advised, along with the textbook on modern spectroscopy written by Hollas.⁷⁶ For the plasma-chemical aspects, especially those related to molecular dynamics and energy dissipation channels, the work of Fridman⁷⁷ is recommended. Finally, the extended database on the atomic spectral lines by Payling and Larkins⁷⁸ is advised for those working with atomic emission lines. For the basic molecular bands, on the other hand, the books of Herzberg⁷⁹ and Pearce and Gaydon⁸⁰ may be of use.

After illustrating the importance of various spectroscopic techniques, let us consider selected methods in detail. For convenience, the diagnostic techniques are subdivided into passive and active, whereas inside each group, brief theoretical notes are given before giving further details.

II. PASSIVE OPTICAL METHODS

Passive methods are based on the radiation spontaneously generated by the excited plasma species, in most cases as a result of electron excitation, not requiring external radiation sources. These methods are completely non-intrusive and relatively easy to implement in the laboratory conditions. The main diagnostic technique in this case is optical emission spectroscopy along with the related methods.

A. Optical emission spectroscopy

1. Theoretical notes

Atoms in the gas excited to high electronic radiative states produce a so-called line emission spectrum.⁷⁰ The intensity of each peak in such a spectrum can be expressed using fundamental parameters of a given optical transition as well as the response of a detector. In most cases, Czerny–Turner or Echelle⁸³ type spectrometers with the corresponding optical detectors can be used for spectral measurements in the laboratory conditions, as schematically shown in Fig. 1(a).

The intensity of an emission line,

I_{i j}

⁠, corresponding to the optical transition between two electronic states

i

and

j

⁠, as shown in Fig. 2(a), can be written as⁷¹

I_{i j} = C (ν_{i j}) h ν_{i j} A_{i j} n_{i},

(1)

where

C (ν_{i j})

is a constant defined by the detection system,

h

is the Planck constant,

ν_{i j} = c / λ_{i j}

is the radiation frequency (⁠

λ_{i j}

is the wavelength),

A_{i j}

is the Einstein coefficient for spontaneous emission, and

n_{i}

is the population of the excited level.

FIG. 2.

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Schematic representation of spontaneous photon emission (a), photon absorption (b), and single (c) and double (d) laser-induced excitation/fluorescence processes. Spontaneously emitted and absorbed photons are drawn by green and red colors, respectively.

If plasma electrons are the main source of excitation, population of the upper state

n_{i}

can be represented as a sum of contributions from the corresponding lower states

k

to the state

i

(⁠

E_{k} < E_{i}

⁠),

n_{i} = \sum_{k < i} k_{k i} n_{k} n_{e} / (A_{i} + Q_{i}),

(2)

where

k_{k i}

is the electron excitation coefficient corresponding to the transition from the

k

to

i

state,

n_{k}

is the population of the state

k

⁠,

n_{e}

is the electron (plasma) density,

A_{i} = \sum_{k} A_{i k}

is the total emission probability of the state

i

⁠, and

Q_{i} = \sum_{x} q_{x}^{i} n_{x}^{i}

is the quenching of the state

i

defined by all contributors

x

in the gas mixture with the quenching coefficients

q_{x}^{i}

and concentrations

n_{x}^{i}

⁠. Let us mention again that, for the sake of simplicity, in the approximation , the population of the level

i

only by the electron impact is considered, neglecting recombination processes as well as possible de-excitation from the upper states.

The electron impact excitation coefficient,

k_{k i}

⁠, can in turn be expressed via the electron energy distribution function (EEDF),

k_{k i} = \int_{E_{0}}^{\infty} f (E) σ (E) d E,

(3)

where

E

is the electron energy,

E_{0}

is the excitation threshold,

f (E)

is the EEDF, and

σ (E)

is the electron impact excitation cross section (as illustrated in Fig. 3). For the sake of simplicity, the Maxwellian EEDF is often assumed in the sputtering discharges corresponding to thermal electrons,

f (E) = 2 \sqrt{\frac{E}{π T_{e}^{3}}} Exp (- \frac{E}{T_{e}}), \int_{0}^{\infty} f (E) d E = 1,

(4)

where

T_{e}

is the electron temperature expressed in eV. For a more precise description, however, possible deviations from the Maxwellian shape in the DCMS⁸⁴ and HiPIMS⁸⁵ cases should be taken into account.

FIG. 3.

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Maxwellian EEDF calculated at $T_{e} = 3$ eV (black line) and the electron impact excitation cross sections for Ar (3s $^{2}$ 3p $^{5}$ 4s $^{3}$ P $_{2}$ ⁠) and O (2s $^{2}$ 2p $^{4}$ $^{1}$ D $_{2}$ ⁠) atomic states (red lines).^81,82

2. Emission spectra

1. Qualitative case

Emission spectra represent an extremely useful source of qualitative information for selective, time-, and space- resolved characterization of the active discharge area as well as the post-discharge, as far as the emission is sufficient. In the case when quantitative information is required, line ratio approaches should be used. On the other hand, when there is no emission in the region of interest, the implementation of active diagnostics is expected, as discussed in Sec. III.

As an example of an emission spectra analysis, the particularities of reactive sputtering in HiPIMS plasma are visualized by the emission spectra acquired at the end of the plasma pulse, as shown in Fig. 4. In this case, the discharge operates with a Ar–O $_{2}$ gas mixture, and the spectra are acquired at low (0.3%) and high (5%) O $_{2}$ admixtures. The first case represents metallic regime of sputtering, since the low oxygen admixture is not enough for complete target poisoning, whereas the second case is related to poisoned regime.⁸⁶ In the first case, sputtering of metal atoms and their ionization is favorable; therefore, the corresponding Ti (around 390–525 nm) and Ti $^{+}$ (320–380 nm) emission lines dominate. The Ar $^{+}$ emission at about 670 nm is also visible, as the discharge current in this case is supported by Ar and Ti ions. At a high oxygen admixture (poisoned regime), the target is covered by a compound layer; almost, no Ti atoms are sputtered, and the current is mainly supported by Ar ions. In this case, the current buildup is also strongly decelerated, revealing a strong peak only at the end of the pulse.⁸⁷ Thus, the corresponding emission spectrum mainly contains Ar emission lines (the red line in Fig. 4) with some traces of Ar $^{+}$ around 430–500 nm. Relatively weak Ar $^{+}$ emission in the poisoned case (compared to Ti $^{+}$ ⁠) is related to several factors, such as the higher ionization potential for Ar and the strong contribution of secondary electrons to the discharge current produced as a result of acceleration of O $^{+}$ ions toward the target at the end of the pulse.⁸⁷

FIG. 4.

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OES spectra acquired at the end of a 50 $μ$ s HiPIMS plasma pulse at low (0.3%, light green) and high (5%, red) O $_{2}$ admixtures to Ar showing redistribution of the main emitters in plasma.

2. Quantitative case (calibrated spectra)

The optical system including an optical fiber (if used), a spectrometer, and a detector may be calibrated by an external light source so that Eq. (1) will be giving an absolute spectral intensity. When a body angle covered by the spectroscopic detection system is known, the spectral emission intensity can be expressed in the units of spectral irradiance (W/m $^{2}$ /Hz or W/m $^{2}$ /nm). This may lead to calculation of the absolute density of emitters in the discharge, $n_{i}$ ⁠. The ground state density can be found in this case as well, if the corresponding excitation constants for each species of interest are known [see Eq. (2)].

The calibration of a spectroscopic system should be realized by a light source with a known spectral radiance profile. For this purpose, the blackbody radiation sources with a known temperature⁸⁸ as well as “nearly” blackbody tungsten-halogen or tungsten-ribbon lamps,⁸⁹ calibration spheres,⁹⁰ or even the solar spectrum⁹¹ may be used.

3. OES imaging

OES imaging is the simplest way to obtain information about the spatial distribution of excited particles in plasma and the only source of two-dimensional information about the plasma processes when active diagnostic methods are not available. The information about the behavior of the individual plasma emission line(s) may also be collected, provided appropriate optical bandpass filters are implemented. The informativeness and straightforward implementation of this technique explain why a majority of optical studies in sputtering discharges were made using either OES or OES imaging. For implementation, an imaging lens should be added to a (synchronized) CCD-based optical detector focused to the volume of interest,²² as shown in Fig. 1(a).

The line-of-sight signal averaging and the accessibility of only excited plasma states (rather than ground states) are two main drawbacks of OES imaging. The former issue can be often solved in case of a spherical or cylindrical discharge symmetry by applying the Abel inversion procedure⁹² to the raw OES data. If the Abel inversion is performed correctly, the information about the excited species in the discharge volume can be obtained, as illustrated in Fig. 5(a) where the distributions of Ti and Ti $^{+}$ excited states in a HiPIMS plasma are shown. Based on these data, the depletion of Ti neutrals above the racetrack and the presence of Ti ions (instead of neutrals) in this region are clearly visible.²⁸ This effect also takes place for the ground state atoms and ions, as discussed in Sec. III B 4.

FIG. 5.

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(a) Spatial distributions of the excited Ti and Ti $^{+}$ atomic species measured by OES imaging in HiPIMS plasma. Reproduced with permission from Hecimovic et al., Plasma Sources Sci. Technol. 21, 035017 (2012). Copyright 2012 IOP Publishing. (b) Spoke rotation (counterclockwise) in a HiPIMS plasma pulse captured by OES imaging. Reproduced with permission from Hecimovic, J. Phys. D.: Appl. Phys. 49, 18LT01 (2016). Copyright 2016 IOP Publishing.

Figure 5(b) demonstrates the appearance of an ionization zone (spoke) in the HiPIMS pulse registered by OES imaging at the same moment of time for Ar, Ar $^{+}$ ⁠, as well as without optical filtering. A clearly elevated Ar $^{+}$ emission at the end of the emission zone in contrast to a rather uniform Ar intensity distribution points out on the ionization nature of a spoke.

Spokes in the HiPIMS pulse also possess different shapes depending on the energy of the upper (excited) state, as studied by OES imaging in the work of Andersson et al.⁹⁴ In this work, under a detailed consideration involving several emission lines in the discharge (corresponding to different excited states), it was shown that the higher the excited level of the corresponding ion emission line, the more compact spokes appear. This fact emphasizes a very high electron excitation at the center of the ionization zone, whereas the electron energy dissipates at the periphery. The fact that ions in the spoke region (and their emission) are not confined in the ionization zone diffusing out of this region has also been demonstrated in several works involving OES^93,94 and streak camera⁶³ imaging.

4. Line ratio methods

The emission line ratios allow accessing a wider range of plasma parameters using emission spectra. This approach requires knowledge of the additional plasma properties, such as the EEDF shape, the excitation cross sections, the self-absorption coefficients, etc., which helps extracting more information in order to study discharge quantitatively.

1. Optical actinometry

The expression used for the emission intensity directly leads to the density of excited states in the discharge, i.e., plasma emitters. However, it might often be necessary to access the ground state density of atoms or molecules, as they represent the majority of plasma species in weakly ionized discharges. In the low-pressure discharges, it is possible using optical actinometry when the known concentration of a reference gas (called actinometer) is added to the gas mixture, and both the electron temperature and electron impact excitation coefficients are known. In this case, the emission line intensity corresponding to the element X with an unknown ground state density, based on Eqs. and , yields

I_{i^{'} k}^{X} = C^{X} A_{i^{'} k}^{X} \frac{h c}{λ_{i^{'} k}} \frac{k_{j i^{'}} n_{j}^{X} n_{e}}{A_{i^{'}} + Q_{i^{'}}},

(5)

where

j

denotes the ground level and the optical transition

i^{'} \to k

is assumed. Similarly, the spectral line intensity of the actinometer A (assuming transition

i^{″} \to l

⁠) yields

(6)

Note that in both cases, electron excitation from the ground states is assumed for simplicity (the so-called corona approximation⁶⁷). After making a ratio between Eqs. and , the GS number density of the species X,

n_{j}^{X}

⁠, can be shortened to

n_{j}^{X} = n_{j}^{A} \frac{I^{X}}{I^{A}} \frac{k^{A}}{k^{X}} β,

(7)

where the other indices are omitted for simplicity and

β

is the transition-specific constant,

β = \frac{C^{A}}{C^{X}} \frac{A^{A}}{A^{X}} \frac{λ^{X}}{λ^{A}} \frac{{(A + Q)}^{X}}{{(A + Q)}^{A}} .

(8)

As we can see, the GS density of interest, $n_{j}^{X}$ ⁠, scales with the actinometer density and the line ratio of X and A species, while it is inversely proportional to the electron excitation coefficient ratio for these species. In the actinometry method, a precise knowledge of the EEDF shape is necessary, which often is a challenge. In order to avoid large uncertainties related to the EEDF profile, close energy levels for the X and A excited states (i.e., $i^{'}$ and ⁠) are normally chosen in order to assure that electrons with the close energy participate in excitation. More details on the assumptions used in optical actinometry are available elsewhere.⁷³

An example of optical actinometry applied to magnetron sputtering is given in Fig. 6, where the number density of ground state O atoms is measured in HiPIMS plasma. In this case, six Ar emission lines have been used for making actinometry ratios using Eq. (7).⁹⁵ A Maxwellian EEDF with the electron temperature of 2 eV is assumed. The obtained result is used for calibration of the O atom density obtained by the two photon absorption LIF (TALIF) method (described below) during the plasma-off time. The discrepancy between the TALIF-based and actinometry-based datapoints may be related to the different electron (⁠ $T_{e}$ ⁠)⁹⁶ and gas (⁠ $T_{g a s}$ ⁠)³⁹ temperature values at the beginning and at the end of the HiPIMS pulse (whereas constant values were assumed for the actinometry datapoints in Fig. 6).

FIG. 6.

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Ground state density of O atoms determined by optical actinometry in HiPIMS plasma (red symbols) and used for calibration of the O density measured by the two-photon absorption LIF (TALIF) technique (gray symbols). The pulse duration is 100 $μ$ s. The pressure is 30 mTorr. Calculated at T $_{e}$ = 2 eV.

2. Effective branching fractions

Another way to determine the ground state number density from emission spectra is based on self-absorption (or re-absorption). This phenomenon takes place in optically thick gaseous media; i.e., when the optical depth (a product of the absorption coefficient and plasma length) is $> 1$ ⁠.⁷⁰ As a result of self-absorption, plasma radiation gets partially trapped by the species of the same kind, giving way for their density determination. Self-absorption is especially pronounced for optical transitions having metastable or ground states as the lower states, as they are normally much more populated than the radiative ones. The idea of self-absorption is known for a long time⁹⁷ and has been used for several applications, including determination of Ar metastables in highly ionized⁹⁸ and other Ar containing discharges.^99,100 It has also been successfully applied for magnetron sputtering.⁴⁰

The effective branching fraction (EBF) method combines re-absorption and line ratio approaches. Density determination in this case is reduced to the measurement of so-called branching fractions related to the optical transitions of interest (the emission line ratio can also be used). The method operates with photon emission rates

Φ_{i j}

⁠, which undergo re-absorption before reaching detection system,⁹⁹

Φ_{i j} \propto A_{i j} n_{i} θ_{i j} = I_{i j} / (C (ν_{i j}) h ν_{i j}),

(9)

where

θ_{i j}

is the so-called escape probability,

I_{i j}

is the line-of-sight averaged emission intensity, and

C (ν_{i j})

is the spectral response of the detector [see also Eq. ].

A branching fraction, in turn, includes the photon emission rates related to different absorbing and same excited states in the following form:

Γ_{i j} = \frac{Φ_{i j}}{\sum_{k} Φ_{i k}} = \frac{A_{i j} n_{i} θ_{i j}}{\sum_{k} A_{i k} n_{i} θ_{i k}} = \frac{I_{i j}^{*} / h ν_{i j}}{\sum_{k} I_{i k}^{*} / h ν_{i k}},

(10)

where summation is performed over several lower states of interest, including the

j

^th one, and

I_{i j}^{*} = I_{i j} / C (ν_{i j})

is the reduced emission line intensity.

As follows from Eq. , when re-absorption is negligible,

θ_{i j} \propto θ_{i k} \propto 1

⁠, and

Γ_{i j}

is defined only by the Einstein coefficient

A_{i j}

⁠. In the presence of re-absorption, however, it is somewhat altered according to the actual optical depth. In order to relate the experimentally measured

Γ_{i j}

to absorbers’ density, the escape factors representing line-of-sight averaged escape probabilities

\bar{θ_{i j}}

^97,99 are used,

Γ_{i j}^{eff} = \frac{g (k_{i j} L) A_{i j}}{\sum_{k} g (k_{i k} L) A_{i k}},

(11)

where

g

is the photon escape factor depending on the optical depth, i.e., a product of the transition-specific absorption coefficient

k

and the effective plasma length

L

⁠. There are several approximations for escape factors in the literature,¹⁰¹ and in the case of uniform excitation and Doppler line broadening, the Mewe’s formula¹⁰² is often used,

g = \frac{2 - Exp (- k_{0} L 10^{- 3})}{1 + k_{0} L} \approx 1 |_{k_{0} L \to 0},

(12)

with

k_{0}

denoting the absorption coefficient at the center of the Doppler-broadened absorption line. A generalized approximation¹⁰³ taking into account the non-uniform emitter distribution as well as collisional broadening may also be considered,

g = \frac{2 - Exp (- c_{1} \cdot τ)}{1 + {(c_{2} \cdot τ)}^{k}},

(13)

where

τ

is the optical depth and

c_{1}, c_{2}

⁠,

k

are the tabulated parameters.¹⁰³ Equation gives better approximations for heavy atoms, such as Xe and Kr.

Since the integral value of the absorption coefficient

\int k (ν) d ν

always scales linearly with the density of absorbers,⁷⁰ the optical depth in either approximation can always be related to this density. In the case of Doppler line broadening,

Δ ν_{D} = 2 \sqrt{2 \ln 2} \cdot \frac{ν_{0}}{c} \sqrt{\frac{R T}{M}},

(14)

(here

c

⁠,

R

⁠,

M

⁠, and

ν_{0}

are the speed of light, gas constant, molar mass, and central line frequency expressed in SI units), the absorption coefficient at the line center,

k_{0}

⁠, obeys the same principle,

k_{0} = \frac{\sqrt{\ln 2}}{4 π^{3 / 2}} \frac{λ_{0}^{2}}{Δ ν_{D}} \frac{g_{i}}{g_{j}} A_{i j} n_{j} \approx 2 \times 10^{- 4} λ_{0}^{3} \sqrt{\frac{m}{T}} \frac{g_{i}}{g_{j}} A_{i j} n_{j},

(15)

where

λ_{0}

is the transition wavelength,

Δ ν_{D}

is the Doppler full width at half maximum (FWHM) of the absorption line,

g_{i}

and

g_{j}

are the degeneracy of levels,

m

is the atomic mass,

T

is the gas temperature, and

n_{j}

is the density of absorbers (SI units are used except for

m

⁠, which is in amu). Finally, a branching fraction can be related to the density of absorbers by combining Eqs. , , and .

In practice, in order to determine populations of N absorbing states, a corresponding number of branching fractions should be involved. The unknown populations can be found step by step, as illustrated in Fig. 7 for three lower states of interest. Three branching fractions should be measured in this case, related to the upper states $i$ ⁠, $i^{'}$ ⁠, and $i^{″}$ ⁠. First (by solving a system of two non-linear equations), the populations of the $x$ and $y$ states can be found, followed by the population of the $z$ state found from additional equation. Note that the level $i^{″}$ may coincide with either of the other two. If an abundant number of spectral lines is available, extra branching fractions may also be used for the sake of statistical data averaging.

FIG. 7.

$Illustration of the determination of three low energy state populations ( x , y , z) by measuring the corresponding branching fractions ( Γ i x , Γ i ′ y , Γ i ″ z) involving three different upper states i, i ′, and i ″.$

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Illustration of the determination of three low energy state populations (⁠ $x, y, z$ ⁠) by measuring the corresponding branching fractions (⁠ $Γ_{i x}, Γ_{i^{'} y}, Γ_{i^{″} z}$ ⁠) involving three different upper states $i$ ⁠, $i^{'}$ ⁠, and $i^{″}$ ⁠.

An example of determination of the Ti ion and the neutral density by the EBF method during a 200 $μ$ s HiPIMS plasma pulse is shown in Fig. 8(a). In this case, populations of three ground state a $^{3}$ F $_{2, 3, 4}$ Ti sublevels are measured.⁴³ The density obtained by EBF and TD-LAS⁵⁴ techniques is compared in Fig. 8(b), showing a very good agreement between these methods. Recent studies on the Ti number density in HiPIMS involving EBF and AAS techniques also confirm good reliability of the EBF method in sputtering discharges⁶⁰ including reactive cases.^44,104

FIG. 8.

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(a) Time evolution of Ti and Ti $^{+}$ number density during a 200 $μ$ s HiPIMS pulse obtained using the EBF method. The pressure is 38 mTorr. (b) Ti number density determined by EBF and TD-LAS techniques as a function of discharge current in DCMS. The pressure is 30 mTorr. Reproduced with permission from Fekete et al., J. Phys. D.: Appl. Phys. 50, 365202 (2017). Copyright 2017 IOP Publishing.

The main advantage of the EBF method is the ability to measure the GS number density dealing with only emission measurements. After the data acquisition, certain post-processing is normally required, involving specially designed software (such as the EBF fit containing the necessary spectroscopic data embedded¹⁰⁵). Among the EBF disadvantages, low sensitivity at low gas pressures (when re-absorption is weak) as well as line-of-sight signal averaging should be mentioned. Nevertheless, a clear detection of the Ti number density of about 10 $^{11}$ cm $^{- 3}$ at 30 mTorr approves the applicability of this method in magnetron sputtering discharges.

3. Electron temperature determination

The Langmuir probe is arguably the most established technique to measure the electron temperature.¹⁰⁶ In the magnetron sputtering discharges, however, the permanent magnetic field as well as a continuous deposition may perturb Langmuir probe measurements.

Alternatively, the line ratio methods can be used for electron temperature determination normally showing good agreement with Langmuir probe data.^68,107 One needs to know the EEDF shape as well as the excitation kinetics of the upper states in order to implement line ratio methods properly.⁶⁸ The corona approximation is often assumed for this purpose considerably facilitating the excitation model.

Once the population mechanism of the upper (excited) state and the EEDF shape are defined, the intensity ratio for the prominent plasma emission lines can be constructed, leading to electron temperature determination.⁶⁸ The line ratio approach should always be adapted to a particular gas mixture. Up to date, $T_{e}$ determination by the line ratio has been realized for the numerous gases, including the hydrogen-containing discharges,¹⁰⁸ single gas discharges,¹⁰⁹ the discharges with a minor addition of foreign gases,¹⁰⁷ for the other gas mixtures.^67,68

From the experimental point of view, similarly to optical actinometry dealing with determination of unknown GS state population if the other GS populations, $T_{e}$ ⁠, EEDF shape, and the excitation cross sections are known [see Eqs. (7) and (8)], the line ratio method targeted at $T_{e}$ determination uses the information about the states’ populations, the electron excitation cross sections, and the EEDF shape. A Maxwellian EEDF is often assumed for simplicity.

In a general form, the ratio

R

of two chosen emission lines corresponding to species X and Y can be expressed via the ground state populations (if the corona model is assumed), electron excitation coefficients

k

depending on

T_{e}

⁠, also implying a certain EEDF profile, in a form [see Eqs. and ],

R \equiv I_{i j}^{X} / I_{k l}^{Y} = f (n_{j}^{X}, n_{l}^{Y}, k_{j i}^{X} (T_{e}), k_{l k}^{Y} (T_{e})) .

(16)

In most cases, such an expression can be easily linearized in the coordinates {Log(⁠

R

⁠), 1/

T_{e}

} within a certain range of

T_{e}

⁠, leading to a semi-empirical formula for the electron temperature. An example of such an expression derived based on two argon emission lines⁶⁸ corresponding to the

3 p_{1}

and

2 p_{1}

Ar excited states (Paschen’s notations are used) is given as

1.73 \cdot Log (R) + 1 / T_{e} + 1.31 = 0,

(17)

where T_e is expressed in eV.

5. Rotational spectral analysis

Apart from the ground state number density and the electron temperature (⁠ $T_{e}$ ⁠), the gas temperature (⁠ $T_{g a s}$ ⁠) is also an important parameter for any sputtering processes. The main reasons for that are as follows: (1) an importance of $T_{g a s}$ control during deposition on a surface for prevention of the surface damage and (2) a necessity to know $T_{g a s}$ for the post-processing of the diagnostics data, for example, for absorption spectroscopy, density estimations, rate coefficients, etc.

There are two main ways of obtaining the gas temperature by emission spectroscopy: via a spectral (Doppler) linewidth and via rotational spectra. In the first case, a high-resolution device with spectral resolution much less than typical Doppler broadening (i.e., sub-pm range) is required. This approach is described in Sec. II B. The rotational analysis involving the rotational temperature (⁠ $T_{r o t}$ ⁠), on the other hand, does not require extra-high resolution and works as far as the rotational molecular bands in the emission spectra can be resolved (1–10 pm range). In this case, the individual populations of rotational states at the excited molecular state can be determined. Even a lower resolution (⁠ $> 10$ pm) is sufficient if the spectral fitting procedure can be applied to the measured spectra.¹¹²

Let us consider the first case as an example. Physically, as a result of a dense rotational structure and a low energy separation between the rotational levels of a molecule, the populations of rotational states are often found in thermal equilibrium with kinetic gas motion. The populations of rotational levels in this case obey the Boltzmann distribution,

\frac{n_{i}}{g_{i}} = \frac{n_{j}}{g_{j}} Exp (- \frac{Δ E}{k T}),

(18)

where

Δ E

is the energy difference between

i

and

j

energy levels,

k

is the Boltzmann constant, and

T

is the gas temperature. From the Boltzmann distribution, the temperature can be restored by measuring the emission line intensities in a rotational band. The relative rotational populations are related to the spectral line intensities,

n_{i} (J) \sim I_{i j} (J) \sim S (J) Exp (- \frac{E (J)}{k T_{r o t}}),

(19)

where

i

and

j

denote electronic states of a molecule,

n_{i} (J)

is the population corresponding to the rotational number

J

in the upper electronic state

i

⁠,

E (J) \sim h c (B J (J + 1) - D J^{2} {(J + 1)}^{2} + \dots

⁠) (with

B

and

D

being the rotational constants) is the energy of the

J

^th rotational state, and

S (J)

is the Hönl–London factor^73,79 responsible for the line intensity distribution in the rotational band. By linearizing the Boltzmann plot in the coordinates

{E (J) / k T_{r o t}, I_{i j} (J) / S (J)}

⁠, the rotational temperature can be withdrawn. Due to the rotational-translational (RT) equilibrium mentioned above, the assumption

T_{r o t} = T_{g a s}

is often used for many gases.

In the low-pressure discharges, one should remember that there is a finite time of RT equilibrium,⁷⁷ which is defined by the collision rate in the gas and may reach several $μ$ s in the mTorr range.³⁹ This might be a limiting factor for the applicability of rotational analysis in pulsed discharges with a short-pulse duration.

An example of the rotational spectrum of N $_{2}^{+}$ molecular ions simulated and measured in magnetron plasma along with the rotational temperature evolution during a HiPIMS pulse obtained with the Boltzmann plot method is given in Fig. 9. It shows a linear temperature growth during the plasma pulse, where the temperature scales linearly with the plasma pulse energy.

FIG. 9.

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(a) N $_{2}^{+}$ (0,0) rotational band simulated and measured in Ar-10%N $_{2}$ -W HiPIMS plasma. For simulation, the rotational constants available from the literature^{73,79,110,111} were used. Shown peak numbers correspond to lower rotational levels. (b) The evolution of $T_{r o t}$ during the plasma pulse measured using two different rotational bands. Pulse duration is 20 $μ$ s. Adapted from Britun et al., J. Appl. Phys. 114, 013301 (2013). Copyright 2013 AIP Publishing LLC.

B. Interferometry

1. Theoretical notes

The resolution of commercial monochromators (0.01–0.1 nm typically) may not be enough for high-resolution measurements of the fine structure or broadening of the emission lines (which is about a few pm or less). Double and triple monochromators may possess only a few times higher resolution, which does not solve the problem completely. A significant increase in spectral resolution can be achieved by interferometry, e.g., using the Fabry–Perot interferometer (FPI), where it lies typically in the range of $10^{- 5}$ – $10^{- 1}$ nm.

FPI is a device introduced by Fabry and Perot in 1897¹¹³ composed of two parallel or confocal high-reflectivity mirrors working as a light cavity (optical resonator) for a certain wavelength.¹¹⁴ In the case of planar mirrors, as a result of multiple reflections in the cavity, constructive interference takes place when the integer number of wavelengths

λ

is equal to the double cavity length, allowing light to escape the cavity at this wavelength. The effective number of reflections in the cavity before light attenuation by the factor 1/

e

is called finesse,

F

⁠. For simplicity, considering only axial light propagation, we can write

n λ = 2 L,

(20)

where

L

is the cavity length and

n

is the order of interference (normally

n ≫ 1

⁠). Constructive interference occurs periodically, leading to the formation of the well-known interference fringe patterns on a remote screen.¹¹⁴ Alternatively, as a result of gradual mirror motion, periodic changes of the axial light intensity (i.e., a central interference spot) may also be observed.³⁶ The light distribution in the fringes is going to be the same if, as a result of the change of either the wavelength or

L

⁠, the condition will be satisfied again. In this case,

n

will change by an integer number. The wavelength increment needed for a

n \to n \pm 1

change is called a free spectral range (FSR) and can be easily calculated by differentiating and assuming

δ L = λ / 2

⁠,

φ \equiv δ λ = \frac{2 δ L}{n} = \frac{2}{n} \frac{λ}{2} = \frac{λ^{2}}{2 L},

(21)

where

φ

is the FSR playing an important role for the FPI resolution, defined via FSR and finesse

F

as

Δ = φ / F .

(22)

The operation of a scanning FPI (i.e., the one with a changeable cavity length) can be represented by an optical bandpass filter having a repetitive transmission function with a period $φ$ and a width $φ / F$ ⁠, as shown in Fig. 10. During the scan, the transmission bands of such a multiband filter shift in the spectral space, letting the peak of interest (located at $λ_{0}$ in Fig. 10) be transmitted periodically with a high resolution. Technically, the FPI mirror motion is typically realized by high-precision piezo-stages.¹¹⁵ Note that both the FPI finesse and resolution depend dramatically on the mirror reflectivity, their surface quality, vibration level, as well as the other factors.¹¹⁴ Let us consider now several FPI implementation schemes.

FIG. 10.

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The principle of a scanning FPI showing the spectral line of interest $f (λ)$ and the periodical FPI transmission function $g (λ)$ moving as a result of changing the cavity length. $φ$ denotes the free spectral range. The arbitrary scale is used.

2. Single-channel case

Since the interference happens independently for each emission line passing through FPI, as far as the condition (20) is satisfied, the optical filtering is required in order to study a separate spectral line with a high resolution. In the simplest case, spectral filtering may be performed by an optical bandpass filter or by a monochromator arranged before or after the FPI, representing a single-channel FPI system shown in Fig. 11(a). In this case, the line spectrum from a plasma source is collimated and transmitted to the FPI mirrors, and after optical filtering and limiting the central spot, light is transmitted to a single-channel detector (e.g., a PMT).

FIG. 11.

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Schematic representation of a planar FPI system with a single-channel detection (a) and a locked-wavelength detection (b). L1 and L2 are the collimating lenses, M1 and M2 are the FPI mirrors, and “Det” denotes the detector.

Let us note that (a) when using a monochromator, its resolution does not play a significant role as far as the spectral line of interest is well separated from its neighbors and (b) the position of the monochromator is not important either as the finally detected signal,

S (λ)

⁠, represents a convolution between the instrumental functions of the FPI,

g (λ)

⁠, and the monochromator,

h (λ)

⁠,

S (λ) = \int_{- \infty}^{\infty} g (λ - λ^{'}) h (λ^{'}) d λ^{'} .

(23)

Since the FPI resolution usually exceeds the one of the monochromator significantly, the FWHM of the final signal $S (λ)$ will be monochromator-limited.³⁶

The drawback of a single-channel FPI operation is the absence of wavelength zeroing. This might be necessary, however, when precise measurements of the absolute wavelength value or the wavelength shift are required (since FPI systems are often exposed to vibrations and temperature drifts). This case is discussed below.

3. Multi-channel cases

The multi-channel FPI measurements may imply either spectral or spatial signal separation, which may be used for zeroing, parallel measurements of the same signal, or simultaneous measurements of several signals, as discussed here.

1. Spectral signal separation

The simultaneous high-resolution measurements of several spectral lines by FPI can be achieved by using monochromators with a CCD-based detector instead of using an output slit with a PMT. In this case, multiple spectral lines can be acquired at the same time and resolved in a high-resolution mode by FPI. The corresponding example is shown in Fig. 12 where three Ti emission lines are measured simultaneously in a DCMS discharge. The spectral resolution along the CCD sensor in this case (“Wavelength” axis) corresponds to the resolution of the monochromator (about 0.05 nm), whereas along the other axis (“FPI airgap, L”), it is defined by the FPI instrumental function (⁠ $\approx 0.02$ pm in this case).

FIG. 12.

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Three Ti emission lines from a DCMS discharge simultaneously detected by FPI with spectral separation. CCD camera is used as a detector. The peak repetition period (FSR) along the “FPI airgap” axis is several pm, whereas the corresponding airgap change is a few hundred nm. The monochromator and the FPI resolution are 50 pm and $\approx 0.02$ pm, respectively.

2. Wavelength lock

One of the wavelengths in the multi-channel scheme described above can be used for wavelength zeroing, provided that it is generated by a separate (stable) light source. This is useful, for example, for the Doppler-shift particle velocimetry.¹¹⁶ A corresponding experimental layout is shown in Fig. 11(b), where a dedicated reference source is used for wavelength zeroing.¹¹⁷ In such a scheme, if no spectral overlap occurs on the detector, the reference line can be used for a precise wavelength determination, even in the presence of a certain temperature drift.³⁷

With a locked wavelength, the velocity distributions of sputtered atoms can be measured, as illustrated in Fig. 13 where the average velocity of Ti and W atoms sputtered in a DCMS discharge is shown. As we can see, W atoms keep the velocity higher than that of Ti (at the same pressure and distance from the target), due to the higher mass and longer momentum conservation during sputtering. At the same time, the Ti atoms lose their energy quicker via collisions with Ar having a nearly zero average velocity already at 50 mTorr.¹¹⁷

FIG. 13.

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Average velocity of the sputtered Ti and W atoms in a DCMS discharge as a function of Ar pressure measured by an FPI with the wavelength locked. Reproduced with permission from Britun et al., Plasma Sources Sci. Technol. 17, 045013 (2008). Copyright 2008 IOP Publishing.

Similar measurements in pulsed discharges would additionally require synchronization between the discharge, the FPI setup, and the detector. In this case, the velocimetry and line broadening under the gas rarefaction in HiPIMS can be studied in detail, representing a challenging task for future research.

3. Spatial signal separation

Not only the central spot in interferogram can be used (as described so far). The spatial signal separation can also be achieved by azimuthal separation of the light channels, using the entire interferogram as a source of information, which can be called “FPI imaging.” One of the first FPI imaging concepts including 6-channel spatial separation has been proposed by Yoshinuma et al.¹¹⁸ A fully operational 4-channel imaging FPI designed for non-repetitive measurements in a fusion plasma has been recently built at the Seoul National University.¹¹⁹ In the last case, azimuthal separation of the interference fringes is realized by a specially designed 5-channel optical fiber with four off-axis channels, and the angular signal processing is performed by a dedicated software. The concept of an FPI with spatial separation might also be useful for simultaneous monitoring of sputtering processes with an advantage of using multiple signal accumulations, which should further improve data reliability.

III. ACTIVE OPTICAL METHODS

Despite the measurement simplicity, passive methods suffer from the line-of-sight optical signal averaging and the impossibility to detect directly the ground state density. Moreover, as the plasma emission in this case is used as a source of information, the passive methods cannot be applied during the plasma-off time of the pulsed discharges. With active diagnostics, these drawbacks are completely or partially eliminated, as discussed below.

A. Atomic absorption spectroscopy

1. Theoretical notes

Photons may be absorbed resonantly by atoms or molecules in the gas. As a result, the absorbers change their electronic state from lower to higher, corresponding to the incident photon energy. The rate of the upper level population as a result of absorption [see Fig. 2(b)] is given via the Einstein coefficient of absorption,

B_{j i}

⁠,

\frac{d n_{i}}{d t} = B_{j i} n_{j} ρ (ν_{i j}),

(24)

where

ρ (ν_{i j})

is the spectral radiation density (expressed in J/m

^{3}

⁠) at the frequency

ν_{i j}

⁠.⁷¹

An external light source used for absorption may have either a continuous or a line spectrum. In the first case after passing through absorbing media (with an absorption peak at wavelength $λ_{0}$ ⁠), the spectrum will be altered in a way shown in Fig. 14. The absorption coefficient at $λ_{0}$ in this case is defined via the initial, $I_{0}$ ⁠, and transmitted, $I_{1}$ ⁠, emission intensities: $k_{0} = 1 - I_{1} / I_{0}$ ⁠.

FIG. 14.

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General representation of the absorption line in a continuous spectrum at the wavelength $λ_{0}$ ⁠. $k_{0}$ denotes the absorption coefficient at the line center.

The light intensity measured after passing through a gas layer with a thickness

L

(⁠

I_{1}

⁠) obeys the well-known Beer–Lambert law,⁷¹

I_{1} (λ) = I_{0} (λ) Exp (- k (λ) L),

(25)

where

k (λ)

is the wavelength-dependent absorption coefficient. Assuming the Doppler profile for

k (λ)

⁠, which is often the case in low-pressure plasmas, we obtain

I_{1} (λ) = I_{0} (λ) Exp (- k_{0} L e^{- \frac{{(λ - λ_{0})}^{2}}{δ^{2}}}),

(26)

where

δ

is the parameter related to the FWHM of a Gaussian profile in the form FWHM

_{G a u s s} = 2 δ \sqrt{\ln 2}

⁠.

Experimentally, the absorption coefficient is often measured by the attenuation of emission line(s) from a reference source after passing through the gas. For this purpose, spectral line detection is normally performed by a monochromator with an intermediate resolution. In this way, the line absorption,⁷⁰ i.e., the signal integrated over a spectral line profile (also called “total absorption”) is acquired,

A_{L} = 1 - \frac{I_{1}}{I_{0}} = 1 - \frac{\int I_{1} (λ) d λ}{\int I_{0} (λ) d λ} .

(27)

Here, the integration is performed over the entire line profile. After substituting Eq. to Eq. and performing certain simplifications,¹²⁰ we obtain

A_{L} = \frac{1}{\sqrt{π}} \int_{- \infty}^{\infty} e^{- x^{2}} (1 - Exp (- k_{0} L e^{- {(α x)}^{2}})) d x,

(28)

where

α

is the broadening ratio between the reference source and plasma spectral lines and

x

is the reduced integration variable.

Since both integral and peak absorption coefficients scale linearly with the density of absorbers,^70,71 based on Eq. , the number density of absorbers,

n_{j}

⁠, yields

n_{j} \approx 10^{12} k_{0} \frac{δ σ_{P}}{f_{j i}},

(29)

where

k_{0}

is in cm

^{- 1}

⁠,

δ σ_{P}

(in cm

^{- 1}

⁠) is the broadening of the plasma absorption line, and

f_{j i}

is the so-called oscillator strength of the absorption line, expressed as⁷¹

f_{j i} = 1.5 \times 10^{- 14} \cdot \frac{g_{i}}{g_{j}} A_{i j} λ_{i j}^{2},

(30)

with

A_{i j}

being in s

^{- 1}

and

λ

being in nm.

Summarizing, the absorption measurements are usually reduced to determination of the peak absorption coefficient $k_{0}$ by measuring the attenuation of the emission line(s), i.e., by acquiring the line absorption $A_{L}$ [see Eq. (27)]. Afterward, the density of absorbers can be calculated by Eq. (29) if the absorption line broadening and the oscillator strength for the chosen transition(s) are known. In order to find $k_{0}$ using the measured $A_{L}$ ⁠, the non-linear expression (28) should be solved numerically. Let us finally note that Eqs. (26)–(29) should be further modified for the non-Doppler broadening cases for rigorous density determination.^121,122

2. Single-channel AAS case

When plasma emission is not negligible [see Fig. 15(a)], the measurable source intensity passing through the plasma (called here

I_{S P}

⁠) contains both the radiation from the reference source (absorbed in plasma) and the radiation generated in plasma:

I_{S P} = I_{a b s . s o u r c e} + I_{P}

⁠. After subtracting the plasma signal from the measured intensity

I_{S P}

⁠, Eq. yields

A_{L} = 1 - \frac{(I_{a b s . s o u r c e} + I_{P}) - I_{P}}{I_{S}} = 1 - \frac{I_{S P} - I_{P}}{I_{S}},

(31)

where the last part of the equation contains only the measurable quantities.

FIG. 15.

Typical AAS implementations in the case of one-by-one (a) and simultaneous (b) signal detection. Adapted from Britun et al., Rev. Sci. Instrum. 86, 123114 (2015). Copyright 2015 AIP Publishing LLC.

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Since the source and the plasma emission cannot be separated during the signal acquisition, they should be measured separately. Moreover, the $I_{S}$ signal must be measured before the absorbers are introduced to the volume of interest. All the $I_{S P}$ ⁠, $I_{S}$ ⁠, and $I_{P}$ signals should be acquired using the same optical geometry.

Absorption measurements normally require long data accumulation. If both the plasma discharge and the reference source are stable, single-channel AAS measurements provide reliable results. The example of the time-resolved number density evolution in HiPIMS discharges measured for Ti neutrals and ions as well as for Ar and Ti metastables is shown in Fig. 16. From these data, several physical effects happening in HiPIMS plasma are clearly visible, such as the depletion of the ground state Ti at the end of the plasma pulse (20 $μ$ s) followed by the Ti and Ti $^{+}$ density increase during the plasma-off time (which corresponds to the arrival of sputtered particles to the volume of measurements), strong excitation of Ar metastables at the end of the pulse followed by their gradual quenching, and finally quite noticeable gas refill starting after 0.3 ms.⁵³

FIG. 16.

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Time evolution of the selected ground state and metastable atomic species in HiPIMS discharges measured by AAS. Pulse duration is 20 $μ$ s. Pressure is 20 mTorr. Reproduced with permission from Britun et al., Plasma Process. Polym. 12, 1010 (2015). Copyright 2015 Wiley.

3. Alternative AAS schemes

1. Dynamic source triggering

Weak intensity of the reference source may result in a high measurement instability of the absorption technique. As shown previously for AAS measurements performed with a gated detector,¹²³ if the plasma emission dominates over the reference source, the standard deviation of the measured

A_{L}

values scales as a square root of plasma to the source intensity ratio,

Δ A_{L} \propto δ_{S} \cdot \sqrt{2 I_{P} / I_{S}},

(32)

where

δ_{S}

is the relative measurement error of the source intensity.

Since $Δ A_{L}$ exceeds 100% already at $I_{P} / I_{S} \approx 50$ (assuming $δ_{S} = 10$ %), increasing the source intensity is very desirable. This is often made using pulsed light sources with a pulse duration in the $μ$ s range. A short-pulse source is normally dynamically synchronized with a gated detector, such as an intensified charge coupled device (ICCD), making possible $I_{S P}$ signal detection only at the moments of the maximum source intensity, thus dramatically improving reliability of the AAS method.

As a result of dynamic source triggering, much lower deviation of the absorption data can be obtained.¹²³ This is illustrated by the time-resolved measurements of the ground state Ti density shown in Fig. 17. In this case, the populations of three Ti ground state energy sublevels are simultaneously detected in HiPIMS plasma [Fig. 17(a)], showing the inversion of the Boltzmann-like population distribution after the plasma pulse. Such inversion is characterized by a positive slope of the corresponding distribution [Fig. 17(b)]. The population inversion in HiPIMS discharges appears as a result of strong excitation of the sputtered neutrals (and to a less extent ions) by hot electrons at the end of the plasma pulse.⁵³

FIG. 17.

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(a) Time evolution of the Ti ground state sublevel population measured in HiPIMS by AAS using dynamic source triggering. (b) The corresponding Boltzmann slopes. Pulse duration is 50 $μ$ s. Pressure is 20 mTorr.

2. Simultaneous signal detection

Both the discharge of interest and the reference source used for absorption may suffer from a current or voltage drift during the measurement time. This in turn may provoke a drift in plasma or/and a source emission intensity. Even a few percent intensity drift may seriously affect the final number density determined by AAS, requiring enhanced stability.

For this purpose, the AAS implementation with a simultaneous detection of the $I_{S}$ ⁠, $I_{S P}$ ⁠, and $I_{P}$ intensities has been proposed,¹²³ as schematically shown in Fig. 15(b). According to this approach, three mentioned emission intensities are measured at the same time; thus, all the potential instabilities get integrated simultaneously into the measured quantities. Technically, however, these measurements cannot be performed using the same channel, and a triple optical fiber should be used. In this way, the equivalent $I_{P}^{*}$ and $I_{S}^{*}$ intensities coming from the side channels are registered, which is followed by calculation of the initial $I_{P}$ and $I_{S}$ signal intensities using the pre-calibrated scaling factors.¹²³

3. Lock-in signal detection

Lock-in detection is a widespread measurement technique proposed in the 1930s,^125,126 which is extremely useful for the low signal-to-noise ratio cases. Using this method, very weak electrical signals with a level much lower than the noise level can be acquired. With the modern lock-in amplifiers, detection can still be reliable when the signal to noise ratio is as low as 10 $^{- 6}$ ⁠.¹²⁷ The extreme sensitivity of lock-in amplifiers is achieved as a result of accepting a very narrow spectral range of the incoming signal, only around a reference frequency, while cutting all the other frequency components around it.¹²⁸

For optical measurements, the incident light intensity is converted to an electrical signal using PMTs, whereas for frequency lock, the light choppers are often used, applicable to the most optical layouts. In the particular case of absorption measurements, the lock-in type detection is especially useful in order to detect a (tiny) attenuation of the source intensity after absorption, i.e., when the $I_{S}$ and $I_{S P}$ signals differ by only a small value. This normally happens when either the density of absorbers is low or the effective absorption length is short. In the case of a non-negligible plasma emission, the corresponding correction should be applied, as discussed previously. A multi-channel detection is readily possible with lock-ins as well. Examples of lock-in-based AAS measurements in optically thin discharges are available in the numerous literature sources.¹²² Among the drawbacks of lock-in detection are (a) single-channel measurements, (b) non-simultaneous signal detection (i.e., results are sensitive to signal instability), and (c) strong requirements to the rotation frequency stability of light choppers.

4. Further remarks on AAS

1. Multi-pass absorption

In the case of an extremely small density of absorbers or a shallow plasma depth, it might be necessary to further increase the sensitivity of absorption. An artificial way of increasing the optical depth is rather widespread in this case. It may be attained by creating multiple (finite) number of reflections of the reference beam inside the plasma reactor¹²⁹ or dealing with an optical cavity where a beam from a reference source may be reflected $N$ times until its intensity is scaled by a factor of $1 / e$ ⁠. In effect, $N$ is the optical finesse of the cavity, which is mainly defined by the reflectivity of the used mirrors (as in the FPI case, discussed above). The latter approach represents a well-known cavity ringdown spectroscopy (CRDS) technique first proposed by O’Keefe and Deacon.¹³⁰ Nowadays, this technique is widely implemented for the numerous applications requiring enhanced absorption sensitivity. Continuous lasers with a narrow linewidth and (often) a tunable emission wavelength as well as pulsed lasers are normally used. The CRDS technique has been successfully applied in the sputtering discharges as well, e.g., for detection of metal particles¹³¹ as well as the small concentration of molecular radicals.¹³² For further reading, we recommend the recent textbook edited by Berden and Engeln¹³³ devoted to this method and integrating numerous applications of CRDS.

2. Role of spectral broadening

AAS measurement with a reference source having a narrow linewidth is rather different from that using a wide linewidth. As far as the broadening of the discharge absorption line remains constant, two limit cases may be considered, as illustrated in Fig. 18. In the first case (top), when the source emission line is much narrower than the plasma absorption line (⁠ $Δ_{S} ≪ Δ_{P}$ ⁠), the source line will be absorbed nearly to the same extent in the center as well as at the periphery without changing its shape. If the peak absorption coefficient is $β$ ⁠, in the described case, the measured line absorption $A_{L} = β$ as well. In this case, a finite width of the absorption profile and convolution with a much broader monochromator instrumental profile will not affect the measured line absorption.

FIG. 18.

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Effect of the reference source and plasma spectral broadening on the line absorption $A_{L}$ in two extreme cases. $β$ denotes peak absorption. Different spectral scales are applied for top and bottom. Adapted from Britun et al., Rev. Sci. Instrum. 86, 123114 (2015). Copyright 2015 AIP Publishing LLC.

The situation is rather different when the source line is much broader than the plasma line [ $Δ_{S} ≫ Δ_{P}$ ⁠; see Fig. 18(bottom)]. In this case, only a central part of the source line undergoes absorption, and, after the convolution with a monochromator, the measured $A_{L}$ value will be much smaller than the apparent peak absorption (⁠ $β$ ⁠). Thus, the situation of a highly broadened (i.e., corresponding to a high temperature), the reference source should be possibly avoided. When this is not possible, high-resolution spectroscopy techniques should be implemented for the $I_{S P}$ signal detection, such as interferometry. An extended analysis of the AAS method for narrow and broad lines is described elsewhere.⁷¹

3. Number density calibration

The importance of the AAS method is its ability to calibrate the ground state density obtained by the other techniques, such as LIF. In highly dynamic and non-uniform discharges, however, special attention should be given to the density calibration.

First, as a result of the line-of-sight signal averaging, only the plasma conditions corresponding to a nearly uniform density distribution should be used for calibration. This is related to difficulties with a correct determination of the effective absorption length, $L$ ⁠, which may appear otherwise.⁵³ Second, the plasma emission may affect the calibration results considerably. As shown in Sec. III A 3, strong plasma emission affects the AAS data stability, which may also perturb the calibration results. Thus, the plasma-off time (in the case of pulsed discharges) or post-discharge conditions are more favorable for correct data calibration. Finally, the plasma-to-source temperature ratio should be carefully considered. The case with a narrow (or at least comparable to plasma absorption FWHM) spectral source is preferable. However, the calibration may still be possible, otherwise, if the high-resolution spectral profiles for both plasma and source are known.

An example of the time evolution of the metal atom density in HiPIMS discharges is shown in Fig. 19 where the AAS datapoints are compared to the line-of-sight averaged density map obtained by LIF imaging (see Sec. III B 4). The LIF data are averaged in the same discharge volume used for AAS [dashed lines in Fig. 1(b)] and calibrated at the end of the plasma-off time. This example shows a satisfactory agreement between the AAS and LIF data evolution. Further details are discussed elsewhere.⁵³

FIG. 19.

View large Download slide

The Ti (a) and Ti $^{+}$ (b) density evolution in HiPIMS discharges measured by AAS and calculated as a result of line-of-sight averaging of the corresponding LIF imaging data. LIF data are calibrated at the end of the plasma-off time. Pulse duration is 20 $μ$ s. Ar pressure is 20 mTorr. Reproduced with permission from Britun et al., J. Appl. Phys. 117, 163303 (2015). Copyright AIP Publishing LLC.

B. Laser-induced fluorescence

1. Theoretical notes

As follows from its name, laser-induced fluorescence is based on detection of the fluorescence light generated as a result of the excitation of certain atomic or molecular electronic states in the gas by external laser radiation. Historically, the fluorescence has been first generated artificially by Wood¹³⁴ using a gas flame with Na lines as an external source, even before the laser invention. The first evidence of laser-induced fluorescence came only in 1975 when Ar metastable ions were detected in a hot-cathode low-pressure discharge.¹³⁵

Fluorescence is a spontaneous emission. By analogy with Eq. , the fluorescence emission intensity corresponding to the transition from the laser-excited upper level

i

to the intermediate level

k

can be expressed as [see Fig. 2(c)]

I_{i k} = C_{1} h ν_{i k} A_{i k} n_{i} .

(33)

In this case, the level

i

is excited as a result of laser photon absorption, and its population can be expressed via the laser intensity and the absorption coefficient

B_{j i}

by integrating Eq. ,

n_{i} = C_{2} B_{j i} n_{j} I_{l a s} / (A_{i} + Q_{i}),

(34)

where

C_{2}

is a constant,

I_{l a s}

is the laser beam intensity, and

A_{i}

and

Q_{i}

are the radiation and quenching losses, respectively. Combining two last equations, the population of the lower state

n_{j}

yields

n_{j} = C \frac{I_{f l u o r}}{I_{l a s}} \frac{(A_{i} + Q_{i})}{h ν_{i k} A_{i k} B_{j i}},

(35)

where

C

is a new constant and the fluorescence intensity is introduced as

I_{f l u o r} \equiv I_{i k}

⁠.

As we can see,

n_{j}

is proportional to the fluorescence signal and inversely proportional to the laser beam intensity. We have to note that Eq. is obtained when a single photon excitation as well as non-saturated laser absorption are assumed, resulting in a linear scaling of

I_{f l u o r}

with the laser intensity

I_{i k} \propto I_{l a s}

⁠. In the case of a saturated or nearly saturated absorption, the linear scaling breaks, resulting in

I_{i k} \propto I_{l a s}^{γ}, where γ < 1.

(36)

In order to increase the fluorescence signal, researchers often work with a nearly saturated LIF signal (as a function of the laser intensity or the pulse energy). In this case, the scaling constant $γ$ is usually determined from the experiment at fixed $n_{j}$ ⁠.

2. LIF-based diagnostics methods

1. LIF spectroscopy

Radiative relaxation (fluorescence) of a laser-excited atomic or molecular state may go via several optical transitions producing multiple emission lines, thus forming a fluorescence spectrum. In the atomic case, such a spectrum normally contains several strong emission lines corresponding to transitions with the highest emission probability. In the molecular case, the situation is similar except for rotational bands are formed instead of atomic lines. In addition, the rotational distribution in the fluorescence emission bands may not always be in equilibrium with the surrounding gas depending on the thermalization constants defined by the molecular radii and the gas pressure,⁷⁷ making fluorescence emission bands generally not suitable for gas temperature determination.

When plasma emission is essential, both the fluorescence and the plasma spectra are registered at the same time, as shown in Fig. 20 where a Ti “emission + fluorescence” spectrum is shown. The Ti fluorescence line at 508.70 nm is clearly visible in this case, corresponding to 3d $^{2}$ (⁠ $^{3}$ P) 4s4p(⁠ $^{3}$ P $^{o}$ ⁠) v $^{3}$ D $_{1}^{o}$ $\to$ 3d $^{3}$ (⁠ $^{4}$ F)4s b $^{3}$ F $_{2}$ atomic transition. The disappearance of this line at the shifted laser wavelength additionally confirms the laser-excited nature of this peak also representing a way for the measurement of the line absorption profile (if the laser line is narrow enough).

FIG. 20.

View large Download slide

The “fluorescence + emission” spectra taken during a HiPIMS pulse at different laser wavelengths showing the intensity changes of the Ti fluorescence line at 508.7 nm. The central excitation wavelength $λ_{0} = 320.584$ nm.⁴⁹ The Ar pressure is 20 mTorr.

LIF spectroscopy is a handy tool in the cases when the plasma emission spectrum is dense and the fluorescence peak(s) of interest cannot be filtered using optical bandpass filters. A monochromator with a resolution higher than the necessary peak separation is required in this case. The drawback of such a detection scheme, on the other hand, is a dramatic decrease in the signal intensity (compared to direct optical filtering) as a result of losses in the light collimation system and in the monochromator. This drawback might be partially compensated using sensitive detectors.

2. Doppler-shift LIF spectroscopy

As shown in Fig. 20, the intensity of any fluorescence line is a steep function of laser wavelength. The reason for this is a relatively narrow (at least in low-temperature discharges) broadening of the absorption line corresponding to the transition of interest. Indeed, a Doppler broadened Ti absorption line at 320.58 nm has a FWHM of only about 0.6 pm at T = 300 K [see Eq. (14)], which can be resolved using a laser with a comparable or narrower linewidth. In the former case, the deconvolution procedure should be applied in order to restore the real profile.

In general, the laser wavelength shift allows visualization of the different groups of particles in the gas corresponding to different velocities along (or opposite) the laser beam direction, which is often called Doppler-shift LIF (DS-LIF). The velocity uncertainty in each group is defined by the laser linewidth. For example, in order to detect the blue-shifted atoms (i.e., those moving toward the laser), the laser frequency (wavelength) should be decreased (increased) in order to “return” to a resonant transition, as sketched in Fig. 21(a). Using this principle, a time-resolved evolution of VDF of the sputtered atoms can be studied. As an example, a clear increase in the VDF width has been detected at the end of a HiPIMS plasma pulse, as shown in Fig. 21(b). In this case, a velocity component parallel to the target surface is implied. Such an increase is explained by the rarefaction of argon above the magnetron target at the moment of the maximum discharge current (the end of the pulse), allowing less collisions for sputtered particles and apparently resulting in a broader velocity distribution.

FIG. 21.

View large Download slide

(a) Illustration of an atom interacting with laser radiation in a still and moving case (blue shift). (b) Broadening of the velocity distribution function measured in a HiPIMS discharge at two distances above the target. Made for the velocity component parallel to the magnetron target surface. Pulse duration is 20 $μ$ s. Pressure is 5 mTorr. Adapted from Britun et al., Plasma Process. Polym. 12, 1010 (2015). Copyright 2015 Wiley.

DS-LIF is useful not only for the thermalized cases (Maxwellian velocity distribution) but also for visualization of the Doppler-shifted groups of atoms in the discharges without thermalization. This situation is often realized in magnetron discharges in the target vicinity. In this case, the DS-LIF imaging technique is normally used, as illustrated below.

3. Narrow laser LIF

Scanning an absorption line profile using a tunable laser with a linewidth considerably narrower than the one of the plasma line (typically Doppler-limited) enables a straightforward determination of the particles’ VDF without deconvolution with the laser profile. For this approach, tunable diode lasers are often used with the line broadening typically less than 0.001 cm $^{- 1}$ ⁠.³⁴ Apart from it, a tunable laser on the Ti:sapphire crystal with a FWHM of about 0.006 cm $^{- 1}$ also represents a reliable solution¹³⁶ applicable to sputtering discharges. In the last work, a two-photon excitation process (described below) was applied to study the O atom absorption profile in this way.

A detailed study on the VDF of the sputtered metal atoms in the DCMS case had been undertaken using a narrow diode laser calibrated by a Fabry–Perot etalon.³⁴ In the last work, a high-resolution velocity distribution of Cr and Al neutrals has been obtained showing the VDF asymmetry both axially and radially depending in the last case on the radial point of measurements. More importantly, a clear separation between the thermalized and non-thermalized sputtered atoms has been demonstrated by the presence of a tail in the measured VDFs (corresponding to non-thermalized atoms) having an average velocity of several km/s. This result corroborates with the VDFs of the sputtered metal particles analyzed by the FPI technique earlier.^37,117

3. Two-photon absorption LIF (TALIF)

If the energy difference between lower and upper states of the optical transition of interest is too large, the corresponding photon frequency (energy) may be outside of the laser spectral range. This issue can be overcome by using a two-photon absorption phenomenon where a (nearly) simultaneous absorption of two photons (with the same or different energies) is expected, as schematically shown in Fig. 2(d). The corresponding technique is called two photon absorption laser-induced fluorescence (TALIF).

Two-photon absorption is a non-linear optical phenomenon, which has been detected experimentally for the first time in a solid state.¹³⁷ As a result of non-linearity, the fluorescence signal scales with the laser beam intensity (or pulse energy) as $I_{f l u o r} \propto I_{l a s}^{2}$ ⁠.¹³⁸ Moreover, the detection threshold for TALIF in terms of the absolute number density is much higher than that for a single photon absorption and estimated¹³⁹ to be only about 10 $^{11}$ cm $^{- 3}$ ⁠.

Classically, two-photon absorption schemes are used for detection of the ground state atoms such as H, N, O, F, C, etc.,^139,140 as well as for the numerous molecules. The O and N cases are especially interesting for sputtering since oxygen and nitrogen are the most common molecular gases used in reactive sputtering. Using TALIF, the evolution of the ground state O atoms in the discharge volume, as well as their time-resolved behavior can be measured. The detection scheme in this case is identical to the one used for single photon absorption.

An example of TALIF-measured O ground state number density behavior in the HiPIMS case (at a fixed time delay) as a function of an oxygen admixture is shown in Fig. 22(a). The excitation of the $^{3}$ P $_{2}$ O state at 225.58 nm followed by fluorescence detection at about 844.6 nm was used. A hysteresis behavior of the O atoms produced in the discharge volume as a function of an O $_{2}$ gas admixture is also clearly detectable, as shown in Fig. 22(b), which is in full agreement with the well-known Berg’s model of reactive sputtering.¹⁴¹ Let us also note that the fluorescence signal level is vanishingly small at low O $_{2}$ admixtures in Fig. 22(b) since nearly all oxygen is trapped on the target surface in this case.

FIG. 22.

View large Download slide

(a) A decay of the O atom number density during the HiPIMS plasma-off time measured by TALIF. (b) The number density of O atoms measured at 300 $μ$ s as a function of an O $_{2}$ admixture showing hysteresis behavior. Pulse duration is 50 $μ$ s. For the hysteresis data pressure is 30 mTorr.

4. LIF imaging

1. Without a Doppler shift

LIF imaging combines the benefits of laser-induced fluorescence and OES imaging techniques. This diagnostic approach allows visualization of the ground state particles in relatively large volumes. LIF imaging combines the ability of the GS particle detection, high time- and space- resolution (ns and sub-mm range, respectively), and two-dimensional density mapping power [see Fig. 1(b)]. Three-dimensional discharge mapping is also possible, as a result of combination of the density maps obtained with 2D imaging. In addition, LIF imaging does not use line-of-sight signal averaging and allows density calibration by the other methods, such as actinometry, absorption spectroscopy,⁵³ etc. The plasma radiation can also be corrected by additional measurements, leading to a virtually perfect tool for multi-dimensional density mapping.^60,61

An example of LIF imaging is illustrated in Fig. 23, where the density distributions of the atomic neutral and ionized Ti sputtered in HiPIMS discharges are shown at two different time delays (counted from the pulse beginning). We can see that during the plasma pulse (at 30

μ

s), both neutrals and ions are distributed in a very non-uniform way. The sputtered atoms exist in the form of neutrals very close to the target as well as above its central part. At the same time, Ti is ionized once entering the ionization zone created by the confined electrons [see Fig. 1(b)]. This results in the elevated ion density in front of the target racetrack observed in Fig. 23. Thus, a depletion of the density of neutrals at 30

μ

s is mainly caused by ionization of the sputtered atoms, as well as their excitation to the upper energy states. We have already seen consequences of these processes in Fig. 5 where the excited Ti neutrals and ions have similar qualitative behavior. After the plasma pulse, the density distributions are getting uniform gradually, as clear from the data obtained at 120

μ

s. The detailed analysis of the described effects can be found in the recent publications related to LIF imaging.^50,60,61

FIG. 23.

View large Download slide

Distribution of the ground state neutral and ionized Ti in HiPIMS discharges at two time delays. The Ar pressure is 20 mTorr. The pulse duration is 50 $μ$ s. The area of about $8 \times 6$ cm is shown (the target diameter is 7.6 cm). Dashed lines indicate the target surface. The red color corresponds to the number density of about $6 \times 10^{12}$ cm $^{- 3}$ for Ti and about $2 \times 10^{12}$ cm $^{- 3}$ for Ti $^{+}$ ⁠. Logarithmic scale is used where 1 color step corresponds to a three-fold density drop.

2. With a Doppler shift

Similarly to LIF spectroscopy, described above, the Doppler-shift approach can also be used in the imaging case. Technically, the experimental setup remains similar to that typically used for LIF imaging, except for changing the laser wavelength corresponding to the Doppler shift of interest. In fact, the DS-LIF imaging method might be considered as a powerful two-dimensional particle velocimetry tool applicable for ground state species. This technique is perfect for time-resolved studies of the dynamically evolving discharges, both qualitatively and quantitatively. The latter case requires calibration, which, for the sake of simplicity, can be performed at the resonant wavelength similarly to the ordinary LIF case.

As an example, the density distributions of the sputtered neutrals in HiPIMS discharges at the very beginning of the plasma-off time registered by DS-LIF imaging are shown in Fig. 24. The imaging has been performed at two symmetrically shifted laser wavelengths corresponding to the horizontal velocity component of atomic Ti equal to about 1.4 km/s. A relatively high Ar pressure (about 75 mTorr) has been used in order to increase the LIF signal intensity. The obtained ground state density maps clearly show that the red-shifted sputtered atoms (moving from left to right in Fig. 24) are mainly grouped in the left side of the racetrack, whereas those moving in the opposite direction are mostly concentrated on the right side. The found spatial density maxima become more blurred at a lower working pressure.^50,124 The found effects may be the result of the combination of the physical particle motion in the discharge and the ground state density depletion and also the charge re-distribution above the magnetron target (happening between Ti and Ti $^{+}$ atoms in this case). This requires decent clarifications, in the future possibly involving complementary diagnostic techniques.

FIG. 24.

View large Download slide

Distribution of the ground state Ti above the target in HiPIMS discharges acquired at two symmetrically shifted laser wavelengths. Preferential particle motion is indicated by arrows. The time delay is 40 $μ$ s. The pulse duration is 20 $μ$ s. The Ar pressure is 75 mTorr. The area of about $10 \times 8$ cm is shown (the target diameter is 10 cm). The dashed line indicates the target surface.

IV. CONCLUDING REMARKS

In this Tutorial, numerous optical diagnostic techniques, which may be of special interest for characterization of sputtering discharges, are described and critically analyzed. The authors were trying to demonstrate certain connectivity between the different methods describing in parallel their theoretical principles, possible ways of implementation, as well as typical results.

We do realize that applying only non-intrusive techniques may not be sufficient for a full understanding of discharge properties. Nevertheless, the superiority of a non-intrusive optical characterization for magnetron sputtering discharges is emphasized in our work. The main reason for this is the fact that as a result of using spectroscopic methods, neither the discharge gets affected by the diagnostic tools nor the measurement results are perturbed by the plasma itself. Another strong point of optical spectroscopy is its high temporal, spatial, and spectral resolution, which typically lies in the ns, sub-mm, and pm (in some cases sub-pm) ranges, respectively.

Based on the discussed methods, one may conclude that a combined implementation of several diagnostic techniques is always beneficial for getting more reliable information about the discharge properties. This might be achieved, for example, by a complementary usage of absorption spectroscopy and interferometry (in order to get the gas temperature for line absorption measurements aiming at number density determination) or by a combination of laser imaging with absorption measurements (in order to build and calibrate a two-dimensional density distribution in the discharge). The suggested complementarity is also visible from the diagnostics examples given in our work. Some of them are summarized below:

the utilization of optical actinometry for calibration of the TALIF data, as illustrated in Fig. 6;
a strong agreement between the branching fraction method and the laser absorption used for ground state density measurements shown in Fig. 8;
complimentary gas temperature measurements realized using different rotational bands, as shown in Fig. 9;
a clear similarity of the time-resolved evolution of the sputtered Ti found by LIF and absorption spectroscopy illustrated in Fig. 19;
a correlation in the sputtered particle velocity values obtained by laser absorption spectroscopy³⁴ and by interferometry;^37,117 and
the density depletion of the neutral atoms (as a result of ionization) found by OES and LIF imaging for the excited and ground states, as illustrated in Figs. 5 and 23, respectively.

We hope that this work can serve as a decent introduction to the spectroscopy methods suitable for characterization of the low-pressure discharges, in particular, those dealing with magnetron sputtering, reasonably combining theoretical, experimental, and technical information for each case.

We also encourage readers especially interested in this field to refer to the additional literature sources, including the corresponding research papers, reviews, as well as fundamental textbooks on plasma spectroscopy.

ACKNOWLEDGMENTS

J.H. acknowledges support of the Ministry of Education, Youth and Sports of the Czech Republic (Project No. LM2018097) and the Czech Science Foundation (Project No. GA19-00579S).

DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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2020

Author(s)

Optical spectroscopy for sputtering process characterization Free

I. INTRODUCTION

A. Characterization of sputtering processes

B. Role of optical diagnostics

II. PASSIVE OPTICAL METHODS

A. Optical emission spectroscopy

1. Theoretical notes

2. Emission spectra

1. Qualitative case

2. Quantitative case (calibrated spectra)

3. OES imaging

4. Line ratio methods

1. Optical actinometry

2. Effective branching fractions

3. Electron temperature determination

5. Rotational spectral analysis

B. Interferometry

1. Theoretical notes

2. Single-channel case

3. Multi-channel cases

1. Spectral signal separation

2. Wavelength lock

3. Spatial signal separation

III. ACTIVE OPTICAL METHODS

A. Atomic absorption spectroscopy

1. Theoretical notes

2. Single-channel AAS case

3. Alternative AAS schemes

1. Dynamic source triggering

2. Simultaneous signal detection

3. Lock-in signal detection

4. Further remarks on AAS

1. Multi-pass absorption

2. Role of spectral broadening

3. Number density calibration

B. Laser-induced fluorescence

1. Theoretical notes

2. LIF-based diagnostics methods

1. LIF spectroscopy

2. Doppler-shift LIF spectroscopy

3. Narrow laser LIF

3. Two-photon absorption LIF (TALIF)

4. LIF imaging

1. Without a Doppler shift

2. With a Doppler shift

IV. CONCLUDING REMARKS

ACKNOWLEDGMENTS

DATA AVAILABILITY

REFERENCES

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Optical spectroscopy for sputtering process characterization