ARTÍCULO DE REVISIÓN

doi: 10.17230/ingciencia.11.21.12

Methods Employed in Optical Emission Spectroscopy Analysis: a Review

Métodos empleados en el análisis de espectroscopía óptica de emisión: una revisión

D. M. Devia ¹, L. V. Rodriguez-Restrepo ² and E. Restrepo-Parra ³

1 Universidad Tecnológica de Pereira, Pereira, Colombia, dmdevian@utp.edu.co.

2 Universidad Nacional de Colombia, Sede Manizales, Colombia, lvrodriguezr@unal.edu.co .

3 Universidad Nacional de Colombia, Sede Manizales, Colombia ereatrepopa@unal.edu.co.

PACS: 52.25.Dg, 31.15.V

In this work, different methods employed for the analysis of emission spectra are presented. The proposal is to calculate the excitation temperature (Texc), electronic temperature (Te) and electron density (ne) for several plasma techniques used in the growth of thin films. Some of these techniques include magnetron sputtering and arc discharges. Initially, some fundamental physical principles that support the Optical Emission Spectroscopy (OES) technique are described; then, some rules to consider during the spectral analysis to avoid ambiguities are listed. Finally, some of the more frequently used spectroscopic methods for determining the physical properties of plasma are described. OES; plasma parameters; Key words: elemental determination; line intensity; broadening; shifting

Resumen

En este trabajo se presentan diferentes métodos empleados para el análisis de espectros ópticos de emisión. El propósito es calcular la temperatura de excitación (Texc), temperatura electrónica (Te) y densidad electrónica (ne) empleando diversas técnicas usadas en el crecimiento de películas delgadas. Algunas de estas técnicas incluyen magnetron sputtering y descargas n arco. Inicialmente, se describirán algunos principios fundamentales que soportan la técnica de Espectroscopía Óptica de Emisión (EOE); posteriormente, se considerarán algunas reglas que deben considerarse para el análisis de espectros con el fin de evitar ambigüedades. Finalmente, se presentarán algunos d los métodos espectroscópicos más determinar las propiedades físicas de plasmas.

Palabras clave: OES; parámetros de plasma; determinación elemental; intensidad de lineas; ensanchamiento; corrimiento

1 Introduction

Plasma diagnostics are the techniques used to obtain information about the nature (properties) of plasma, such as the chemical compositions and species of the plasma, density of the plasma, plasma potential, electron temperature, ion/electron energy distributions, ion mass distributions and neutral species [1],[2]. Some of the techniques employed for the characterization of plasma include the Langmuir probe [3],[4], interferometry [5], mass spectroscopy [6], the Thompson dispersion method [7] and optical emission spectroscopy (OES) [8]. The most direct plasma characterization technique that requires low theoretical analysis is likely the Thompson dispersion method; however, the spectroscopy technique is the simplest if the instrumentation permits the use of it. Spectroscopic methods for plasma diagnostics are the least perturbative, and for the evolution of the plasma parameters, they study the emitted, absorbed or dispersed radiation [9]. Generally, spectral diagnostic methods attempt to establish relationships between the plasma parameters and the radiation features, such as the emission or absorption intensity and the broadening or shifting of the spectral lines. The applicability of these methods depends on the system that is being studied because some of the techniques are general and others are not easily applied in total and local thermodynamic equilibrium. Many studies in the literature on plasma parameters use the OES technique, which can be applied in many fields, from spatial plasmas [10] to laboratory experiments such as nuclear fusion [8] and plasma-assisted material production [11]. OES is a very useful technique in materials processing because the plasma features can be correlated with the characteristics of the material. Furthermore, OES is employed as a control tool during the process to control contamination and to enable time and spatial monitoring of the plasma. G. Zambrano and E. Restrepo et al [12] performed plasma studies on a magnetron sputtering discharge implemented for the production of WC/DLC multilayers with a mixture of Ar/CH₄. The information gained from the plasma spectrum obtained during the production process allowed the species contained in the plasma and their densities to be determined. These parameters were subsequently correlated with the structure and composition of the films. E. Restrepo and A. Devia analyzed the properties of plasma that was produced in a pulsed vacuum arc system. The system was used to grow TiN coatings. In this work, the electron temperature and density were determined using spectroscopic techniques, including the lines-continuum ratio, line-line ratio and Stark broadening techniques. L.A García et al [13] studied the parameters of a pulsed arc plasma using the electrostatic probe and OES techniques. This plasma was used for growing DLC coatings. Values of T_e and n_e were obtained by both techniques. H. Jiménez et al [14] characterized the plasma used in the production of T_iO2 thin films by the pulsed arc technique. Again, different spectroscopic methods were used to determine the parameters of the plasma. Many studies performed by other authors can be found in the literature. For example, Yong M. Kim et al [15] studied the nitrogen behavior in a DC plasma nitriding process. To establish a suitable process control, the densities of the active nitrogen species must be monitored because they are responsible for the ferro/metal reactions. Using OES, the authors observed the nitrogen concentration with respect to hydrogen. Hassan Chatei et al [16] studied a microwave H₂ − CH₄ −N₂ plasma used for the deposition of diamond films in continuous and pulsed mode using the OES technique. In the continuous mode, an actinometrical OES technique was used for determining the tendency of H, CH and CN species concentration. The authors concluded that important information about the transition phases and the different excitation processes can obtained using the optical measurements, and the results indicated that the electronic excitation process was predominant. Because of the great utility of spectroscopic techniques in the study of plasma and its applications, some important basic concepts are addressed in this document, which provides insight on some of the most widely used spectroscopic methodologies for the characterization of plasma. These methodologies include line-to-line relationships and line broadening. To use spectroscopic techniques in an appropriate manner, it is necessary to have certain expertise and knowing some useful tips for identifying the species, choosing the lines for the calculations and selecting the most suitable method. By using these methods, the substances present in the plasma can be identified, and parameters such as the excitation temperature (Texc), electron temperature (Te) and electron density (ne) can be determined. In addition to the description of the methods, examples of the application of the methods are presented in this work.

2 Fundamental concepts

2.1 Total thermodynamic equilibrium

2.2 Maxwell's law

This law describes the distribution of the particles that compose the plasma with respect to their velocities. The density, dN, of any type of particles that have velocities in the v+dv range can be described as dN=Nf(v)dv, where Nis the density of the species of particles considered and f(v) is the Maxwell velocities distribution function: 

where k is Boltzmann's constant, which has a value of 1.38 10 ^{− 23}J/K m is the mass of the particle and T is the temperature [18].

2.3 Boltzmann's law

where E₁ and E₂ are the energies of levels 1 and 2, g₁ and g₂ are the statistical weights of the energies of levels 1 and 2 and T is the temperature.

The statistical weight or state density (g₁) of a state of energy E₁ is related to the quantum number J₁, which corresponds to the total kinetic moment of the i-th level through the relationship gi = 2J_i + 1 [19].

It is interesting to express the density of particles, N_i, of the i-th level as a function of the total relative density of all levels sum N_i = N. Using , the following equation was obtained

where T is the average temperature of the electrons in the i-th energy state and the partition function [17], which is written as: 

This function acts like a normalization factor that ensures the fulfillment of equation (2).

2.4 Saha equation

U_z+1T and U_zT are the partition functions of the ions with charge (Z+1)e and Ze, respectively, h is Planck's constant (6.626 ×10⁻³⁴ J.s), is the mass of the electron (9.109×10⁻³¹ Kg), Ez∞ is the ionization energy and is the minimum ionization energy.

2.5 Local thermodynamic equilibrium

Under these conditions, it is possible to use the LTE concept. In this concept, the electron distribution function is assumed to be Maxwellian at each point in the plasma with respect to the electronic temperature (Te) [22]. Ocassionally, considering partial local thermodynamic equilibrium (PLTE) is better. For a large number of elements and for hydrogen, the transversal collision sections decrease and transition probabilities increase as the fundamental level is reached [23]. For the LTE concept to hold in a plasma, the collisions with electrons must dominate over the radiative processes, which requires a sufficiently large electron density. A criterion proposed by McWhirter [24] was based on the existence of a critical electron density where the collisional rates are at least ten times the radiative rates. For an energy gap difference (∆E) between the transition levels, the criterion for LTE is [25]: N_e ≥ 1.6x10¹²T^1/2(∆E)³ cm^− 3.

2.6 Partial local thermodynamic equilibrium

3 Spectral line characteristics

3.1 Spectral line intensity

An emission line is defined as the energy emitted per second and it depends on the probability of transitioning between the two involved energy levels and their electron population. In thermodynamic equilibrium, the population distribution of the i−th level, N_i(E_i), is given by the Boltzmann distribution, which is presented in eq. (2). In a stationary field, the total absorption rate, N₁B₁₂I(v), that represents the number of absorbed photons per volume per second must be equal to total emission rate N₂B₂₁I(v) + N₂A₂₁ because of the energy conservation law. N₁ and N₂ represent the population of levels 1 and 2, I( ν) is the spectral intensity, and A₂1, B₂1 and B₁2 are the Einstein coefficients of spontaneous emission, induced emission and absorption, respectively [27].

The Einstein coefficients can be written as , y 

where c is the speed of light and f₁2 is the strength of the oscillator; therefore, 

then, 

By replacing eq. (3) 

By using eq. (2) for two different transitions and establishing a relationship between the transitions, the following is obtained: 

where 

where I₂1 is the line intensity and v₂1 is the transition frequency. By replacing (2) and evaluating eq. (15) with i = 2, the spectral line intensity can also be described as: 

where g₂ is the density of states, E₂ is the upper level energy and T is the excitation temperature.

3.2 Spectral line broadening

3.3 Natural broadening

During a transition, the electron provides the energy that corresponds to the difference between two atomic levels. According to the Heisenberg uncertainty principle and the small lifetime of the excited states, the energy levels are not exactly defined, which results in the energy of the emitted photon presenting an error [29]. As is well known, the transition energy and frequency are directly related, which produces an uncertainty in the frequency that is reflected in the line broadening. The profile generated as a consequence of natural broadening is given by: 

where I_N(ν) is the spectral line intensity due to the natural transition energy, I_o is the maximum intensity, ν_o is the central frequency and β is a constant. The natural broadening is Lorentzian type, which is characterized by greater tails. This broadening has typical values on the order of 0.01 pm in units of wavelength.

3.4 Doppler broadening

The random movement of emitted atoms relative to the spectrometer causes a broadening known as Doppler or sometimes called temperature broadening, which introduces a Gaussian profile [30].

where δν_D is the broadening of the spectral line due to the Doppler effect given by: 

where I_D(ν) is the line intensity, R is the ideal gas constant (8.31451[J/K.mol]) and M is the mass of the atom or ion.

3.5 Pressure broadening, coalitional or stark broadening

Atomic collisions can produce a Lorentzian profile in the lines. The Stark effect results in a shift or division of the spectral lines into several components due to the presence of an electrical field. This effect is analogous to the Zeeman effect, which also produces broadening but is caused by a magnetic field. The Stark effect is produced by collisions of charged particles that have a permanent, strong dipole moment. A strong and chaotic electric field produces Stark broadening, and a static electric field induces shifting. The pressure dependence can be described from the damping due to collisions [31].

where I_s(v) is the line intensity and C is a constant

3.6 Instrumental broadening

3.7 Real broadening

(i) If a line is primarily broadened by the Stark effect and instrumental broadening, which generates a Lorentzian profile, the real broadening can be approximately obtained from [33]:

where is the Full Width at Half Maximum (FWHM)

(ii) If the line has a predominant Doppler broadening, which has a Gaussian profile, the real width is given by: 

(iii) If the line has contributions from not only the Stark effect but also Doppler broadening, the FWHM can be calculated as 

4 Some spectroscopic techniques

4.1 Spectral lines identification

(i) There are some errors introduced by instrumentation that has a certain resolution. For example, if a device has a resolution of 0.2 nm, and the spectral line is theoretically placed at 538.0337 nm (C I – neutral carbon) [33], the spectrometer can present the line between 538.2337 nm and 537.8337 nm.

(ii) Another difficulty caused by the instrumental resolution is the impossibility of separating two lines that have differences that are less than the resolution (instrumental broadening). In this case, the lines overlap and they appear as one line, which makes using signal deconvolution techniques necessary.

(iii) Although the emission wavelength (frequency) values of a substance are like a fingerprint, it does not avoid the presence of radiation emission of several substances at closer wavelengths with differences (∆λ) less than the instrument resolution. For instance, NI (neutral nitrogen) emits radiation at 600.8473 nm, and CI (neutral carbon) emits at 600.718 nm. In this case, ∆λ=0.1293 nm; if the instrument resolution is 0.2 nm, is less than the resolution, which makes determining if the line belongs to carbon or nitrogen impossible. (iv) There are physical reasons that produce a shift in the spectral lines. An example is the shift caused by the Stark effect or by pressure, as was stated previously. To avoid these problems, the spectroscopists may look for solutions that allow these problems to be solved at the moment the spectral lines are identified. Some tips are presented in the following:

Before performing the experiment, collect a spectrum of a light source of a monoatomic substance that belongs to a known element. Use the database and observe the reported lines present in the spectrum. If there is a shift, try to calibrate the equipment until the shift becomes the lowest. Repeat this procedure at the beginning of each experiment. In addition to calibrating the equipment, this procedure will enable you to identify the shift produced by the instrument.

Some transitions between energy levels occur with higher probabilities than others. Therefore, the spectral lines at these wavelengths are intense. If you have doubts identifying one spectral line, especially if it belongs to a certain substance, it could be expected that the other lines of this substance with high intensity appear in the spectrum.

An example is presented in the following. Hydrogen emits several lines at the wavelength shown in Table 1. In this table, the relative intensities of these lines are also included. The lines at 434.042, 486.129, 486.127 and 656.29 nm [33], [34] can likely be hidden because of noise or by other lines. Nevertheless, the lines at 410.176, 434.049, 486.136, 656.27 and 656.285 nm [33], [34] appeared with significant intensities and could be identified in the emission spectrum when hydrogen was present in the analyzed substance.

To ensure that the line set belongs to certain material, the distances between the lines may be measured; they have to be compared with the distances of the lines in the database and they may be similar. Despite the lines shifting and broadening caused by different factors, the distances between the lines must be similar to those reported in the database.

When lines that do not belong to any of the expected substances appear in the spectrum. For example, in a reactor, some hydrocarbides, such as methane and acetylene, are introduced, and the spectrum is expected to contain C, H, CH, and so on. If there are other elements or substances, they are likely contaminants such as oxygen nitrogen steel or cobalt, some of which belong to the material employed in the reactor construction and others, such as those in the air that cannot be totally evacuated during the vacuum process.

For measuring the line broadenings that are different from the instrumental broadening and thus determining several physical characteristics of plasma from these broadenings, a high-resolution instrument is required, if possible, at scales beyond nanometers.

5 Experimental setup

6 Results and discussion

6.1 Atomic and molecular spectral lines

Spectra of a plasma generated during the production of YBaCuO coatings (a) spectrum with narrow and symmetric lines that corresponds to neutral argon and (b) spectrum showing the asymmetry and the high broadening of the lines, which indicate that they are produced by the molecular transition of nitrogen (N2)

6.2 Excitation temperature

To calculate the excitation temperature, the line-to-line ratio method was used [38]. The Boltzmann plot can be used, according to eq. (15). By rewriting eq. (16), the spectral line intensity can be written as: 

N, h, c and U are the same for all of the atomic lines; therefore: , and 

where 

Plotting 

A curve is obtained with a slope of m = − 1 /k_Texc This method is widely used in the literature [39]. For obtaining a better understanding, two different transitions between energy states, m-n and p-n, were considered; the first transition occurs between levels m and n, where m is the upper level and n is the level with lower energy. The spectral line intensity is:

The second transition is between energy levels p and n, where p is the level with upper energy and n is the level with lower energy; the line intensity is given by:

Correlating these spectral lines, the next equation is obtained: 

By performing a variable substitution, we obtain: , where 

A line with slope -1/kT_exc was obtained, and T_exc can be subsequently calculated. The excitation temperature, T_exc, is defined for a population of particles via the Boltzmann factor. Therefore, the excitation temperature is the temperature where a system with this Boltzmann distribution is expected. However, this parameter only has physical meaning when the system is in local thermodynamic equilibrium [40]. Figure 3(a) presents the plot used for determining the excitation temperature for the experiment conducted at a pressure of 0.04 Ar/0.02 O2 with a substrate temperature of 550 ºC and a power of 80 watts. The excitation temperature, T_exc, was 3921.29 K.

Figure 3(a) Plot used for determining the excitation temperature for a plasma generated during the production of YBaCuO coatings at a pressure of 0.04 Ar/0.02 O2 with a substrate temperature of 550 ºC and a power of 80 watts and (b) The Ar I line at 810.369 nm for determining Te using the ratio line-to-continuum.

6.3 Electron temperature using the line-to-continuum ratio.

where ni and ne are the ion and electron densities, respectively, Z_i, is the ionic partition function, m is the electron mass, T_ion is the ion temperature, E_i is the ionization energy and ∆E_i is the lower ionization potential. If the factor N/U(T) is replaced from Eq. (16) to Eq. (34), the following relation is obtained:

As observed, there are two temperatures. For a system close to local thermodynamic equilibrium (LTE), T_ion=T_e, can be assumed; nevertheless, T_exc can continue being an independent variable that is obtained separately, which allows the other parameters to be calculated. The emission coefficient of the continuum radiation is given by [41], [42]:

If a relation between (35) and (36) is performed and is expressed as a function of wavelength, then:

Experimentally, ε_c is measured closet to the line chosen, and both are presented in arbitrary units. From Eq. (37), T_e is calculated. In this case, the experiment implemented for the production of YBaCuO coatings using the magnetron sputtering technique is again employed. For this purpose, choosing a line and finding the corresponding parameter for that line is necessary. Therefore, the Ar I line at 810.369 nm was chosen to obtain the intensity, and the area under the curve could be calculated. In contrast, integrating the continuous intensity is not necessary because it is automatically integrated by the apparatus. In Figure 3(b), the line chosen for determining T_e using the ratio line-to-continuum is presented. For calculating the electron temperature, the values listed in Table 2 must be replaced, and the electron temperature obtained previously is also used. The obtained electron temperature is 0.3 eV (3481.8 K). The continuum value was taken on the proximities of the line (exactly under it).

6.4 Electron density using the ratio between lines with the different degree of ionization method

Finding the relation between intensities of this pair of lines from Eq. (31) and (32), the following is obtained: 

Where 

The population ratio between the states is given by the Saha Equation. In the case of consecutive ionized states, this equation is: 

By replacing (32) in (33), the following is obtained 

where the subscripts a and i indicate the atomic and ionic variables, respectively. By isolating the density, the following expression is obtained: 

Figure 4(a) presents the lines chosen for the electron density calculation. Values of the variables employed in the corresponding calculation for each pair of lines are given in Table 3.

6.5 Electronic density from the stark broadening method

One of the most widely used spectroscopic techniques for determining the electronic density results from the Stark broadening of measured spectral lines. The radiative particles perturbation increase is caused by the electrical fields produced by the environmental electron and ions. In this method, the absolute intensities are not required, only the relative lines shape and width. For densities n_e ≥ 10¹⁵cm ^{− 3}, the broadening is high, and standard spectrometers and monochromators are sufficient. Once the line shapes are determined, the ne value is obtained by comparing the real and theoretical spectral lines width or shape. Details regarding quantum mechanics theory, lines profile shape computation and data tabulations can be found in the text by Griem [43]. The well-isolated Stark line broadening in non-hydrogenic neutral and single ionized atoms (such as lithium and once ionized barium) is dominated by the electronic effect. Then, the full width at half maximum (FWHM) of these lines can be calculated using the electronic impact approximation and corrected by the important ionic quasiestatic broadening; a shift in the line centers (usually toward higher wavelengths) is present far from the normal position. For a good approximation (20 o 30), the medium broadening ∆λ_1/2 is given by [44].

In this expression, the width is measured in Å and the density in cm ^{− 3}. The parameter N_D represents the number of particles in a Debye sphere and is given by: 

ependent, and they have low fluctuations with respect to the electronic temperature. This formula is applied to lines produced from neutral atoms. To apply this model to single ionized atoms, it is necessary to replace the numeric coefficient 3/4 by 1.2. For all of the lines (different atoms and ions), this expression is useful in the range of N_D ≥ 2 and 0.05 < A( n_e/10¹⁶ )^1/4 < 0.5. When N_D is less than the given value, the calculation of cuasistatic field, which includes shielding and correlation, are not applicable. When A is outside of the given range, the width and shifting may be determined from the line profile. A list of W (electronic contribution), A (ionic contribution) and D (shifting constant) parameters are given by Griem for several lines of different neutral atoms, from helium to cesium, and single ionized atoms, from lithium to calcium, as shown in [45], [46]. As explained in section 2.3, the total line profile is a combination of different effects. As an example of an experimental application, a study of plasmas generated using a pulsed arc discharge for growing ZnO coatings was performed. To separate the influence of each effect, the instrumental broadening was measured, and a value of 0.1 nm was obtained. Doppler broadening was determined using the Eq. (13), but this value was two orders of magnitude less than the instrumental broadening, which is almost neglecting. To obtain the Stark broadening, Eq. (15) was used with an instrumental broadening of 0.1 nm and a FWHM equal to 0.14 nm, and a value of 0.4 nm was obtained for the Stark broadening. Because the Griem constants are reported by [47] for temperatures of 5.000, 10.000 and 20.000 K, and the experimental temperature is approximately 8100 K, it is necessary to perform an extrapolation. This extrapolation is shown in Figure 4(b). The values employed for creating this figure are presented in Table 4 for the O II (oxygen single ionized) line at 518 nm. With this procedure, we obtained ne on the order of 8 x10¹²cm ^{− 3}.

7 Conclusions

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