Study of the layer thickness of multilayer sample by the LIBS method based on ablation rate correction

Abstract

As a remote and in situ diagnostic technique for the first wall of tokamaks, laser-induced breakdown spectroscopy (LIBS) has shown promising potential for depth profile analysis of deposition layers on plasma-facing components (PFCs). However, due to the complexity of the interface of deposition layers and the limitations of laser profiles, achieving an accurate deposition layer thickness is often more difficult for an in situ LIBS system in tokamaks. In previous studies, a Laser Profile & Interface Roughness model (LPIR model), which considers the laser beam profile and interface roughness factors, has been developed to identify the interface of deposition layers. In this study, the effect of ablation rates from different materials in the deposited layers on the accuracy of their thickness has been investigated. The depth profiling of a Ni–Cu–Ni–Cu multilayer sample, which has a four-layer structure, has been carried out using the LIBS technique under different focusing conditions as well as various laser pulse energies, with the pressure maintained at 10⁻⁵ mbar. The LPIR model was used to reconstruct the depth distribution profile of the Ni–Cu–Ni–Cu multilayer sample and quantify the interfacial positions of the deposited layers. A layer thickness correction method for multilayer sample is proposed based on the dependence of the ablation rates of different layers on laser fluence. The correction ability has been evaluated based on the relative errors between the calculated and the scanning electron microscope (SEM) values for different layer thicknesses. The relative errors of the corrected layer thicknesses are all significantly improved, and the accuracy of the layer thicknesses has been substantially improved. The proposed method will not only help us better understand the LIBS depth profiling of multilayer samples under different laser fluence conditions, but it will also further improve the accuracy of the layer thickness analysis of multilayer samples. This result is of positive significance for the application of in situ LIBS diagnostics in plasma–wall interaction (PWI) studies.

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1. Introduction

During the tokamak discharge process, plasma-facing components (PFCs) are subjected to high heat, radiation, and high energy particle fluxes, leading to problems such as fuel retention, erosion, deposition of impurity elements,^1,2etc. The plasma–wall interaction (PWI) seriously threatens the PFCs' performance and the tokamak device's steady-state operation.^3,4 Therefore, an efficient diagnosis of impurities and residual fuel in PFCs is required to monitor the source of impurities and to understand the erosion mechanism and deposition process, which has been a critical issue for the safe and reliable operation of tokamak devices. In particular, in situ analysis of deposition layers with accurate diagnosis of layer thickness is vital for us to monitor issues such as impurity deposition patterns.^5–8

Laser-induced breakdown spectroscopy (LIBS) has attracted much attention in the field of nuclear applications due to its advantages of real-time, in situ, non-intrusive, and rapid multi-element analysis.^6,9–11 In the field of nuclear fusion, LIBS is considered to be the most promising method for in situ diagnostic analysis of PFCs in fusion devices, and LIBS diagnostic studies for various fusion devices have been carried out extensively over the past two decades. For example, research on the LIBS diagnostic method for the Experimental Advanced Superconducting Tokamak (EAST),^12–15 KSTAR,¹⁶ Wendelstein 7-X (W7-X),^17,18 Frascati Tokamak Upgrade (FTU),^19–21 Joint European Torus (JET)^22–24 and other devices has achieved exciting results in the investigation of key issues such as fuel retention, optimization of key parameters, impurity distribution, etc. Several research efforts have demonstrated that LIBS is a promising technique for depth profiling of deposition layers, which can be used to diagnose erosion and impurity deposition on PFCs, which can be analyzed either post-mortem or in real time.^25–32 A recent study has achieved the first spatially resolved isotope measurements of Li using the LIBS technique,³³ and although this is challenging, the depth profiling of isotopes also demonstrates the advantages of LIBS for in situ diagnostics of tokamak devices. In the process of depth resolution of the deposition layer using the LIBS technique, the accuracy of the layer thickness has always been a major concern for researchers. Especially during in situ LIBS diagnostics, the harsh experimental conditions and the complexity of deposited layers will affect the determination of the ablation rate and interface location, leading to difficulties in analyzing the thickness of the deposited layers. Sun et al. investigated boron impurity deposition on the surface of tungsten (W) samples from the diverter region of the KSTAR using the LIBS technique and quantified the depth distribution of boron impurities using intensity accumulation.³⁴ Liu et al. applied the ex situ LIBS technique to obtain the elemental distribution and depth distribution of a deposition layer on graphite tiles of the HL-2A device. They combined this with the correlation coefficient method to determine the thickness range of the deposition layer.³⁵ Manard et al. used the LIBS technique for depth profiling of particle-like nuclear fuel with a three-layer structure, distinguishing layers and locating the interfaces using Pearson's correlation coefficients.³⁶ To minimize the influence of thermal effects and improve the depth resolution, Favre et al. used the picosecond LIBS technique for the depth resolution of the W layer on a CuCrZr substrate, and satisfactory results were obtained.³⁷ Imran et al. studied the depth profiles of tungsten coatings, and the results were very close to the standard values at lower laser fluences.³⁸ Li et al. investigated screws in the baffle region of the diverter module of W7-X using the picosecond LIBS technique, which was combined with the interface position determined by the correlation coefficient method to achieve the diagnosis of the thickness of a carbon deposition layer.³⁹ In addition, in our previous work,⁴⁰ we proposed a method for determining the interface position based on the Laser Profile & Interface Roughness model (LPIR model), which also achieves a more accurate diagnosis of the thickness of the Ni layer. However, most of the experimental studies have been carried out on single-layer deposition samples. There are fewer studies for depth resolution of complex multilayer samples that simultaneously consider the interfacial position and the ablation rate behavior of the deposition layers.

In this work, depth profiling of the Ni–Cu–Ni–Cu multilayer sample was performed using the nanosecond LIBS technique at 10⁻⁵ mbar pressure. The depth distribution profiles of the Ni–Cu–Ni–Cu multilayer sample were obtained at different laser fluences. Based on the ablation rate of Ni and Cu as a function of laser fluence, we describe and demonstrate a novel method to correct the layer thickness of a multilayer sample and the accuracy of the corrected thickness of each layer is significantly improved.

2. Experimental

2.1. Material sample

The multilayer sample that has a four-layer structure used in this experiment was prepared using the electroplating method. The cross-sectional structure of the Ni–Cu–Ni–Cu multilayer sample obtained using a scanning electron microscope (SEM) is shown in Fig. 1. The multilayer sample consists of pure Ni and pure Cu alternately. From the surface to the substrate, the first layer on the surface is a pure Ni layer, the second layer is a thicker pure Cu layer, and the third layer is a thin pure Ni layer. Finally, Cu exists as a substrate, and the first three layers have been named the Ni-layer, Cu-layer, and Ni-2 layer, respectively. From the SEM results, the thicknesses of the Ni-layer, Cu-layer and Ni-2 layer are 5984 ± 352 nm, 9092 ± 1023 nm and 2468 ± 336 nm, respectively.

Fig. 1 Cross-sectional morphology and elemental distribution imaging of the Ni–Cu–Ni–Cu multilayer sample.

2.2. LIBS setup

The device diagram of the LIBS diagnostic system for the Ni–Cu–Ni–Cu multilayer sample in a vacuum environment is shown in Fig. 2, which consists of equipment such as a laser, vacuum system, spectrometer, computer, optical lenses, and others. A 1064 nm Nd: YAG laser was used as an excitation source with a pulse duration of 5 ns and a repetition frequency of 2 Hz. A vacuum pumping system was used to maintain the experimental pressure in the vacuum chamber at 10⁻⁵ mbar. The laser beam passes sequentially through an λ/2 waveplate and prism splitter and is then focused onto the sample by a focusing lens (d = 100 mm and f = 500 mm) on an optical rail. A specially designed fiber bundle was used to collect the generated plasma through a collection lens (d = 54 mm and f = 100.8 mm) at 15° from the sample's normal direction. The output of the fiber bundle was connected to a spectrometer (Shamrock 750, Andor, grating: 1200 grooves per mm) equipped with an ICCD (iStar 340T, Andor). The center wavelength of the spectrometer was set to 508 nm, and the detection range was 498.69–517.38 nm. The bundle comprises 19 fibers, which are arranged in a circular and linear arrangement at the input and output ports of the bundle, respectively, and the core diameter of a single fiber is 300 μm. The gain was set to 1000, and the delay and integration times were 100 ns and 5 μs, respectively.

Fig. 2 The schematic diagram of the LIBS experimental setup.

It is well known that the influencing factors of laser fluence are the laser energy of a single pulse and the area of the laser spot. Therefore, in our experiments, two schemes are adopted to obtain different laser fluences, as shown in Fig. 2. Plan-A was to achieve different laser fluences by varying the spot size. The laser energy was set to 170 mJ, and the spot area was varied by changing the position of the focusing lens along the normal direction of the sample. ΔL was defined as the difference between the focusing lens-to-sample distance and the focal length of the lens, i.e., the distance from the focal point to the sample. When ΔL = 0 cm, the laser beam was focused on the surface of the sample, and ΔL > 0 cm indicates that the laser beam was focused below the surface of the sample. It is worth noting that the spot size becomes progressively more significant as ΔL increases. In addition, the spot size variation on both sides of the focal point shows a basically symmetric trend, so the case where the laser is focused above the sample's surface is not discussed in this experiment. Plan-B is to obtain different laser fluences by varying the laser energy under fixed focusing conditions, using a waveplate/polarizer combination for adjusting the laser energy, which were 64 mJ, 88 mJ, 100 mJ, 120 mJ, 150 mJ, and 170 mJ, respectively.

2.3. Correction algorithm

In the region of interest of laser fluence, based on the dependence of the ablation rate of pure Ni and pure Cu materials on the laser fluence, we will correct the thicknesses of the Ni-layer, Cu-layer, and Ni-2 layer, respectively. The specific methodology consists of the following procedures:

(i) Firstly, the ablation rates of the Ni layer and the Cu layer should be provided separately as the standard ablation rate, which can be obtained using eqn (1) and (2),

where AAR_Ni and AAR_Cu represent the standard ablation rate of the Ni layer and the standard ablation rate of the Cu layer, respectively, and h_n denotes the depth of the ablation crater produced by n laser pulses.

(ii) The second step of the correction procedure is to obtain the ablation rate distribution functions Δh_Ni(F) and Δh_Cu(F) for the Ni layer and Cu layer under different laser fluences (F). The Δh_Ni(F) and Δh_Cu(F) can be obtained based on the dependence of the ablation rate on the laser fluence for the pure material and the standard ablation rate of procedure (i).

(iii) The final procedure is the calculation of the corrected layer thickness using the formulae represented by eqn (3) and (4):

d_Ni = Δp_Ni × Δh_Ni(F) (3)

d_Cu = Δp_Cu × Δh_Cu(F) (4)

3. Results and discussion

3.1. Spectral analysis

Fig. 3 shows the typical LIBS spectra of the deposited layer elements Ni and Cu for different numbers of laser pulses at ΔL = 2 cm, a laser energy of 170 mJ, and standard analytical spectrum lines used for depth profiling. The corresponding spectra for other different ΔL conditions are shown in Fig. S1.† The spectral lines in the spectra were identified according to the NIST database.⁴¹ In accordance with Fig. 3, we can see that the observed emission lines are consistent with the constituent elements of the sample. The trend of the intensity of the emission lines of Ni and Cu elements is negatively correlated, and the spectra recorded at the top of the sample contain only the emission lines of Ni element; similarly, the spectra at the substrate of the sample contain only the emission lines of Cu element, which corresponds to the unique Ni–Cu–Ni–Cu multilayer structure of the sample. In the range of pulse numbers n, 20 < n < 50, the increase and decrease in the emission line intensities of both Cu and Ni elements are gradual, which is caused by the non-uniformity of laser energy distribution and the interface roughness. In addition, the standard analytical spectral lines for elemental Ni and Cu must be rigorously selected, so that they can be used for the whole series of experiments, i.e., the emission lines with the highest possible spectral intensities and sufficiently good signal-to-noise ratios are selected as the analytical spectral lines for elemental Ni and Cu, i.e., Ni I 503.537 nm and Cu I 515.32 nm.

Fig. 3 Typical spectra of the Ni–Cu–Ni–Cu multilayer sample under different numbers of laser pulses at ΔL = 2 cm and a laser energy of 170 mJ. (a) Ni I 503.537 nm. (b) Cu I 515.32 nm.

3.2. Depth resolution of the Ni–Cu–Ni–Cu multilayer sample under different ΔL conditions

For a multilayered sample, when the laser is shot repeatedly at the same location on that sample, the intensity of the emission signal of the characteristic elements of each layer as a function of the number of laser shots provides a depth profile of the multilayered sample. In plan-A of this experiment, we first kept the laser parameters such as laser wavelength, frequency, and pulse width unchanged, the laser energy of a single pulse was set to 170 mJ, and the depth resolution of the Ni–Cu–Ni–Cu multilayer sample under different laser fluences was realized by adjusting the difference between the focusing lens-to-sample distance and the focal length of the lens (ΔL). The relationship between the ablation crater diameter and laser fluence at different ΔL is shown in Table 1. In our experiments, the smallest ablation crater with the maximum laser energy density was obtained at the focal position (ΔL = 0 cm), and with the increase of ΔL (overfocusing), the larger the ablation crater diameter, the lower the laser fluence. The ablation crater size increases from 0.40 mm to 0.98 mm, and correspondingly, the laser fluence decreases from 135.28 J cm⁻² to 22.54 J cm⁻². In our previous work, we developed a depth-resolved numerical model based on the laser shape factor a and the interfacial roughness factor σ of layered samples, named the LPIR model.⁴⁰ By using this model, it is possible to reconstruct the LIBS depth distribution profile and also to localize the interface position. The feasibility of the model was verified using two-layer samples, and the accuracy of the interfacial position localization method proposed based on the model was improved. In another part of our recent work, we further extended the LPIR model to the simulation of multilayer samples under different ΔL, and the calibration results of the laser shape factor a for different ΔL are also given in Table 1. Fig. 4 illustrates the LIBS depth distribution profiles of the Ni–Cu–Ni–Cu multilayer sample with different ΔL and the numerical simulation results of the LPIR model, demonstrating good agreement between the experimental and modeling results. The interface locations between different layers were further determined from the depth distribution profiles of the Ni–Cu–Ni–Cu multilayer sample, as well as the numerical simulation results. The quantitative results for each interface location at different ΔL are shown in Table 2. As can be seen from eqn (5), the interfacial position of the multilayer sample is crucial for the calculation of the layer thickness,

d_i = Δp_i × AAR (5)

where d_i is the thickness of the ith (i = 1, 2, 3) layer, AAR is the average ablation rate of the sample, and Δp_i is the number of laser pulses corresponding to the ith layer. Δp_i is calculated using eqn (6), where interface_i is the interface location for the ith layer.

Δp_i = interface_i − interface_i−1 (6)

Table 1 The dimensions of ablation craters, laser fluences, and shape factor a at different ΔL

ΔL (cm)	Ablative crater diameter (mm)	Laser fluence (J cm^−2)	a
0	0.40	135.28	2.05
1	0.44	111.80	2.02
2	0.51	83.22	2.00
3	0.61	58.17	1.83
4	0.73	40.62	1.64
5	0.82	32.19	1.50
6	0.89	27.33	1.49
7	0.98	22.54	1.46

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Fig. 4 Depth distribution profiles and simulation results of the Ni–Cu–Ni–Cu multilayer sample at different ΔL. (a) ΔL = 0 cm. (b) ΔL = 1 cm. (c) ΔL = 2 cm. (d) ΔL = 3 cm. (e) ΔL = 4 cm. (f) ΔL = 5 cm. (g) ΔL = 6 cm. (h) ΔL = 7 cm.

Table 2 Quantitative detection of the interfacial positions of the Ni–Cu–Ni–Cu multilayer sample at different ΔL

ΔL (cm)	Interface1 (Δp1) (pulse)	Interface2 (pulse)	Δp2 (pulse)	Interface3 (pulse)	Δp3 (pulse)
0	10	20	10	25	5
1	11	22	11	27	5
2	21	38	17	46	8
3	32	60	28	73	13
4	53	106	53	129	23
5	72	164	92	191	27
6	92	218	126	253	35
7	119	290	171	336	46

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In particular, when i = 1,

Δp₁ = interface₁ (7)

It is important to note that the results in Table 2, that is, Δp₂ ≤ Δp₁ for smaller ablation craters (when ΔL < 5 cm), but in terms of layer thicknesses, the result of Section 2.1 is d₂ > d₁.

This result suggests that a uniform sample average ablation rate will not accurately characterize the layer thickness at higher laser fluences. The difference in ablation rates between different layers appears to be more pronounced at higher laser fluences. In other words, this difference in ablation rates should be corrected for accurate layer thickness calculations. The specific correction method will be described in detail in Section 3.4.

3.3. Depth resolution of the Ni–Cu–Ni–Cu multilayer sample at different laser pulse energies

To validate the above results, we implemented plan-B to perform depth resolution of the Ni–Cu–Ni–Cu multilayer sample at different laser fluences by varying the laser pulse energies, which were set to 64 mJ, 88 mJ, 100 mJ, 120 mJ, 150 mJ, and 170 mJ. The focusing condition was set to ΔL = 2 cm for each laser pulse energy. We investigated the effect of the laser pulse energy on the ablation craters and fitted the corresponding ablation crater profiles to obtain shape factors a for the simulation of the depth distribution, as illustrated in Fig. 5. The diameter of the ablation craters increased slightly with the increase in laser pulse energy. The corresponding laser fluences ranged from 56.14 J cm⁻² to 84.54 J cm⁻². Based on the above results, the depth distribution profiles of the Ni–Cu–Ni–Cu multilayer sample under different laser pulse energies were obtained. The simulation and reconstruction of the depth distribution profiles of the Ni–Cu–Ni–Cu multilayer sample were also carried out based on the shape factors a. The experimental results and simulation results are shown in Fig. 6. Fig. 6 illustrates that the depth distribution profiles with obvious layered structures were obtained for all laser pulse energy conditions at ΔL = 2 cm, and the multilayer distribution characteristics of the Ni–Cu–Ni–Cu sample became more evident with the decrease of the laser pulse energy. Two effects of increasing the laser pulse energy should be noted. Firstly, as expected, the number of laser pulses required to destroy the deposited layer decreases with increasing energy, which corresponds to an increase in the ablation rate, and secondly, for both the Cu-layer and the Ni-2-layer, the depth distribution profiles exhibit a gradual increase and gradual decrease, which are asymmetric. The dominant factors of this asymmetric phenomenon were summarized as the factor of the non-uniformity of the laser energy distribution and the factor of the interfacial roughness of the layered sample.⁴⁰ Similarly, according to our proposed interface position localization method, we determined the interface positions of the Ni–Cu–Ni–Cu multilayer sample under different laser pulse energy conditions, and the results of the interface positions of each layer are presented in Table 3. Also, the results of Δp_i calculated according to eqn (6) are included in Table 3. We can clearly find that Δp₂ ≤ Δp₁, which is consistent with the phenomenon in Section 3.2, i.e., when we performed depth resolution of the Ni–Cu–Ni–Cu multilayer sample and calculated the layer thicknesses under a higher laser fluence, the use of the uniform average ablation rate of the Ni–Cu–Ni–Cu multilayer sample could no longer meet the demand for accurate calculations. We speculate that this is closely related to the evolutionary behavior of ablation rates for different materials at different laser fluences.

Fig. 5 Cross-sectional profile and shape factor fitting results of ablation craters at laser energies of (a) 64 mJ, (b) 88 mJ, (c) 100 mJ, (d) 120 mJ, (e) 150 mJ, and (f) 170 mJ, respectively.

Fig. 6 Depth distribution profiles and simulation results of the Ni–Cu–Ni–Cu multilayer sample at laser energies of (a) 64 mJ, (b) 88 mJ, (c) 100 mJ, (d) 120 mJ, (e) 150 mJ, and (f) 170 mJ, respectively.

Table 3 Quantitative detection of interfacial positions of the Ni–Cu–Ni–Cu multilayer sample at laser energies of 64 mJ, 88 mJ, 100 mJ, 120 mJ, 150 mJ, and 170 mJ, respectively

Energy (mJ)	Interface1 (Δp1) (pulse)	Interface2 (pulse)	Δp2 (pulse)	Interface3 (pulse)	Δp3 (pulse)
64	35	70	35	84	14
88	31	57	26	69	12
100	28	51	23	64	13
120	26	46	20	57	11
150	23	41	18	51	10
170	21	38	17	46	8

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3.4. Layer thickness calibration method

As discussed previously, the interfacial position and the ablation rate of the Ni–Cu–Ni–Cu multilayer sample are two essential factors in achieving an accurate calculation of the layer thickness. The precise calibration of the ablation rate of all layers under different laser fluences is necessary since the accuracy of the interface location localization method based on the LPIR model has been verified. We have investigated the ablation rate as a function of laser fluence for pure Ni and Cu materials under the same experimental conditions. The relationship between the ablation rate and laser fluence for pure Ni and pure Cu materials is shown in Fig. 7. For the ablation rate of the pure Ni material, the ablation rate increases approximately exponentially with the increase of laser fluence, and the fitted curve was described using an exponential function with the fitting coefficient R² = 0.998, while for the ablation rate of the pure Cu material, the ablation rate in the region of interest of the laser fluence (30 J cm⁻² < F < 130 J cm⁻²) exhibits a linear increase with the increase of laser fluence, and the fitted curve was described using a linear equation described by the fitting coefficient R² = 0.988. As described in Section 2.3, Δh_Ni(F) and Δh_Cu(F) can be obtained based on the dependence of the ablation rate on the laser fluence for the pure material from Fig. 7 and the standard ablation rate of the procedure (i). As demonstrated in Fig. 8, the red line represents Δh_Cu(F), which was obtained by linear fitting, and the blue line represents Δh_Ni(F), which was obtained by exponential fitting. In addition, the average ablation rate of the sample that was not corrected is also shown in Fig. 8, denoted by the black line.

Fig. 7 The variation of the ablation rate of the (a) pure Ni material and (b) pure Cu material with different laser fluences.

Fig. 8 The average ablation rate of the Ni–Cu–Ni–Cu multilayer sample, and the standard ablation rate distribution function of the Ni layer and Cu layer at different laser fluences.

Verifying the feasibility of this correction method is essential. Considering this, the layer thicknesses before and after the correction based on the interfacial positions of the Ni–Cu–Ni–Cu multilayer sample under different ΔL were calculated. The thickness results of each layer before and after the ablation rate correction are shown in Fig. 9. The results of layer thicknesses calculated using the ablation rate correction method for different ΔL conditions are significantly closer to the SEM values. In order to intuitively reflect the correction level of the method, Fig. 10(a–c) show the results of the relative error (Re) between the calculated values and the SEM values before and after correction for the thickness of the Ni-layer, Cu-layer and Ni-2 layer, respectively. The dashed lines in Fig. 10 represent the confidence intervals (Re_SEM) for the layer thicknesses, which are 5.88%, 11.25%, and 13.61% for the Ni-layer, Cu-layer, and Ni-2 layer, respectively. It should be noted that the SEM values and confidence intervals for the thicknesses of each layer are derived from the results of Section 2.1. The results of the calculated values of the layer thicknesses are considered to be reliable when Re < Re_SEM. It is apparent from Fig. 10 that the relative errors of the layer thicknesses obtained using the uncorrected average ablation rate are significant and mostly deviate from Re_SEM. In contrast, the relative errors of the layer thicknesses calculated according to eqn (3) and (4) are significantly improved, especially for the Cu layer, where the corrected results are all convincing. In addition, although a few instances of overcorrection occur, i.e., the relative error after correction is slightly larger than the relative error before correction, the results of the layer thickness calculations are still reliable when compared to Re_SEM. For the Ni layer, the results of the corrected layer thickness are also accurate without considering the two more extreme conditions (ΔL = 0 cm and ΔL = 7 cm). Considering the extreme conditions (ΔL = 0 cm and ΔL = 7 cm), there may be several reasons for the significant relative error in layer thickness. For ΔL = 0 cm, the diameter of the ablation crater is the smallest and the laser fluence is the highest. In this case, redeposition of the Ni material may occur on the inner wall of the ablation crater, which will additionally provide a spectral signal of Ni element. Since the source of this spectral signal is the redeposition behavior of the Ni material that occurred during the ablation process rather than the actual Ni layer, it can adversely affect the calculation of the Ni layer thickness. In addition, the thermal effects at the higher laser fluence should not be ignored. For ΔL = 7 cm, the ablation crater is enormous, the laser fluence is lower, and the lower ablation rate tends to result in inefficient ablation. In addition, the larger spot may result in an increased inhomogeneity of the laser energy distribution, and these conditions may not be suitable for the depth resolution of thicker deposited layers. Using the aperture to control the spot size and adjusting the laser fluence by varying the energy may improve the results of LIBS depth profiling. Overall, the results for layer thicknesses with ablation rate correction are significant, which initially validates the feasibility of the method.

Fig. 9 Layer thickness results before and after correction with different ΔL. (The SEM values for each layer thickness are also presented in the figure, and shadow areas indicate the layer thicknesses with the error ranges for the Ni layer, Cu layer and Ni-2 layer, respectively).

Fig. 10 Comparison of the relative errors of the layer thickness before and after correction for different ΔL: (a) Ni layer, (b) Cu layer, and (c) Ni-2 layer.

The experimental results of plan-B were used to validate the adaptability and accuracy of the layer thickness correction method further. Combining the results of the interface positions in Table 2 and eqn (3) and (4), we directly calculated the thicknesses of the Ni layer, Cu layer, and Ni-2 layer. The calculated layer thicknesses of the Ni layer, Cu layer and Ni-2 layer under different laser energy conditions are shown in Table 4, and the relative errors between the calculated and SEM values are also included in Table 4. As can be seen from Table 4, the maximum relative errors of the calculated values for Ni layer thickness, Cu layer thickness, and Ni-2 layer thickness are 5.74%, 10.85%, and 11.68%, respectively. By comparing Re with Re_SEM, the results in Table 4 indicate that all the thickness calculations of the Ni layer, Cu layer and Ni-2 layer are trustworthy. The ablation rate distribution functions Δh_Ni(F) and Δh_Cu(F) are further proved to be effective and accurate. It means that the ablation rate distribution functions Δh_Ni(F) and Δh_Cu(F) can be directly used to calculate the layer thickness, which provides an idea for the thickness analysis of similar samples.

Table 4 Calculated results and relative errors of layer thickness for the Ni–Cu–Ni–Cu multilayer sample obtained using the layer thickness correction method at different laser pulse energies

Energy (mJ)	Ni layer		Cu layer		Ni-2 layer
	Calculated value (nm)	Re (%)	Calculated value (nm)	Re (%)	Calculated value (nm)	Re (%)
64	5641	5.74	10 078	10.85	2224	9.87
88	5851	2.23	9086	0.07	2265	8.24
100	5936	0.80	9062	0.33	2756	11.68
120	6314	5.51	8979	1.24	2671	8.23
150	6054	1.16	8695	4.36	2632	6.65
170	6078	1.57	8920	1.89	2315	6.18

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4. Conclusion

In this study, we performed depth profiling of a Ni–Cu–Ni–Cu multilayer sample using the LIBS technique at different laser fluences under a vacuum environment of 10⁻⁵ mbar and calculated the thickness of each layer. We proposed a method of layer thickness correction by analyzing the behavior of the ablation rate for pure Ni and pure Cu materials at different laser fluences obtained experimentally, and combining this with the standard ablation rate of various layers. We established a distribution function of the ablation rate related to the laser fluence for each layer and used it as a basis to realize the correction of the layer thickness of the Ni–Cu–Ni–Cu multilayer sample. Two sets of independent experiments verified the feasibility and accuracy of the method. The results show that the LPIR model combined with ablation rate correction substantially improves the accuracy of layer thickness measurement of LIBS on multilayer samples. The ablation rate distribution functions Δh_Ni(F) and Δh_Cu(F) of different materials can help us understand the ablation process under different laser fluences more comprehensively and select appropriate experimental conditions to meet different experimental requirements. More importantly, in the in situ LIBS analysis of fusion devices, with the help of the ablation rate distribution functions Δh_Ni(F) and Δh_Cu(F), the thickness of the deposition layer can be obtained quickly and accurately. It is of great importance and positive significance to provide reference ideas for in situ LIBS application in fusion devices.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Shiming Liu: methodology, data curation, investigation, and writing – original draft. Cong Li: conceptualization, writing – review & editing, funding acquisition, and supervision. Qi Hi: investigation. Huace Wu: investigation. Xiaohan Hu: investigation. Boliang Men: investigation. Ding Wu: funding acquisition. Ran Hai: funding acquisition. Xingwei Wu: funding acquisition. Hongbin Ding: resources, funding acquisition, and project administration.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12375203 and 12375208), National Key R&D Program of China (No. 2019YFE03080100, 2022YFE03200100, 2023YFF0714901, and 2023YFF0714903), and National Natural Science Foundation of Liaoning province (No. 2023MS098).

References

1. J. Roth, E. Tsitrone, A. Loarte, T. Loarer, G. Counsell, R. Neu, V. Philipps, S. Brezinsek, M. Lehnen, P. Coad, C. Grisolia, K. Schmid, K. Krieger, A. Kallenbach, B. Lipschultz, R. Doerner, R. Causey, V. Alimov, W. Shu, O. Ogorodnikova, A. Kirschner, G. Federici and A. Kukushkin, J. Nucl. Mater., 2009, 390, 1–9.
2. M. Lehnen, A. Alonso, G. Arnoux, N. Baumgarten, S. A. Bozhenkov, S. Brezinsek, M. Brix, T. Eich, S. N. Gerasimov, A. Huber, S. Jachmich, U. Kruezi, P. D. Morgan, V. V. Plyusnin, C. Reux, V. Riccardo, G. Sergienko, M. F. Stamp and J. E. Contributors, Nucl. Fusion, 2011, 51, 123010.
3. J. W. Coenen, M. Berger, M. J. Demkowicz, D. Matveev, A. Manhard, R. Neu, J. Riesch, B. Unterberg, M. Wirtz and C. Linsmeier, Nucl. Mater. Energy, 2017, 12, 307–312.
4. G. Janeschitz and I. Jct, J. Nucl. Mater., 2001, 290, 1–11.
5. A. Huber, B. Schweer, V. Philipps, N. Gierse, M. Zlobinski, S. Brezinsek, W. Biel, V. Kotov, R. Leyte-Gonzales, P. Mertens and U. Samm, Fusion Eng. Des., 2011, 86, 1336–1340.
6. V. Philipps, A. Malaquias, A. Hakola, J. Karhunen, G. Maddaluno, S. Almaviva, L. Caneve, F. Colao, E. Fortuna, P. Gasior, M. Kubkowska, A. Czarnecka, M. Laan, A. Lissovski, P. Paris, H. J. van der Meiden, P. Petersson, M. Rubel, A. Huber, M. Zlobinski, B. Schweer, N. Gierse, Q. Xiao and G. Sergienko, Nucl. Fusion, 2013, 53, 093002.
7. Q. M. Xiao, A. Huber, V. Philipps, G. Sergienko, N. Gierse, P. Mertens, R. Hai and H. B. Ding, J. Nucl. Mater., 2014, 455, 180–184.
8. G. S. Maurya, A. Jyotsana, R. Kumar, A. Kumar and A. K. Rai, Phys. Scr., 2014, 89, 075601.
9. C. Li, C. L. Feng, H. Y. Oderji, G. N. Luo and H. B. Ding, Front. Phys., 2016, 11, 114214.
10. G. S. Maurya, A. Marín-Roldán, P. Veis, A. K. Pathak and P. Sen, J. Nucl. Mater., 2020, 541, 152417.
11. E. H. Kwapis, J. Borrero, K. S. Latty, H. B. Andrews and K. C. Hartig, Appl. Spectrosc., 2024, 78, 9–55.
12. Z. Hu, N. Gierse, C. Li, P. Liu, D. Zhao, L. Sun, J. Oelmann, D. Nicolai, D. Wu, J. Wu and H. Mao, Phys. Scr., 2017, T170, 014046.
13. P. Liu, D. Y. Zhao, L. Y. Sun, C. L. Fu, J. M. Liu, C. Li, R. Hai, C. F. Sang, Z. H. Hu, Z. Sun and J. S. Hu, Plasma Phys. Controlled Fusion, 2018, 60, 085019.
14. C. Li, D. Zhao, Z. Hu, X. Wu, G. N. Luo, J. Hu and H. Ding, J. Nucl. Mater., 2015, 463, 915–918.
15. D. Y. Zhao, C. Li, Z. H. Hu, C. L. Feng, Q. M. Xiao, R. Hai, P. Liu, L. Y. Sun, D. Wu, C. L. Fu, J. M. Liu, N. Farid, F. Ding, G. N. Luo, L. Wang and H. B. Ding, Rev. Sci. Instrum., 2018, 89, 073501.
16. M. Kim, M. S. Cho and B. I. Cho, J. Nucl. Mater., 2017, 487, 305–310.
17. C. Li, N. Gierse, J. Oelmann, S. Brezinsek, M. Rasinski, C. P. Dhard, T. S. Pedersen, R. König, Y. Liang, H. Ding and C. Linsmeier, Phys. Scr., 2017, T170, 014004.
18. D. Zhao, R. Yi, A. Eksaeva, J. Oelmann, S. Brezinsek, G. Sergienko, M. Rasinski, Y. Gao, M. Mayer, C. P. Dhard and D. Naujoks, Nucl. Fusion, 2020, 61, 016025.
19. S. Almaviva, L. Caneve, F. Colao and G. Maddaluno, Phys. Scr., 2016, 91, 044003.
20. S. Almaviva, F. Colao, M. Iafrati, S. Lecci, L. Laguardia and G. Maddaluno, Spectrochim. Acta, Part B, 2023, 206, 106715.
21. S. Almaviva, L. Caneve, F. Colao, V. Lazic, G. Maddaluno, P. Mosetti, A. Palucci, A. Reale, P. Gasior, W. Gromelski and M. Kubkowska, Fusion Eng. Des., 2021, 169, 112638.
22. A. Semerok, D. L'Hermite, J. M. Weulersse, J. L. Lacour, G. Cheymol, M. Kempenaars, N. Bekris and C. Grisolia, Spectrochim. Acta, Part B, 2016, 123, 121–128.
23. J. Karhunen, A. Hakola, J. Likonen, A. Lissovski, M. Laan, P. Paris and J. E. Contributors, J. Nucl. Mater., 2015, 463, 931–935.
24. C. Grisolia, A. Semerok, J. M. Weulersse, F. Le Guern, S. Fomichev, F. Brygo, P. Fichet, P. Y. Thro, P. Coad, N. Bekris, M. Stamp, S. Rosanvallon and G. Piazza, J. Nucl. Mater., 2007, 363, 1138–1147.
25. P. Paris, M. Aints, A. Hakola, M. Kiisk, J. Kolehmainen, M. Laan, J. Likonen, C. Ruset, K. Sugiyama and S. Tervakangas, Fusion Eng. Des., 2011, 86, 1125–1128.
26. M. Suchoňová, P. Veis, J. Karhunen, P. Paris, M. Pribula, K. Piip, M. Laan, C. Porosnicu, C. Lungu and A. Hakola, Nucl. Mater. Energy, 2017, 12, 611–616.
27. L. Mercadier, A. Semerok, P. A. Kizub, A. V. Leontyev, J. Hermann, C. Grisolia and P. Y. Thro, J. Nucl. Mater., 2011, 414, 485–491.
28. P. G. Bhat, P. Veis, A. M. Roldán, J. Karhunen, P. Paris, I. Jõgi, A. Hakola, J. Likonen, S. Almaviva, W. Gromelski and M. Ladygina, Nucl. Mater. Energy, 2023, 37, 101549.
29. V. Dwivedi, A. Marín-Roldán, J. Karhunen, P. Paris, I. Jõgi, C. Porosnicu, C. P. Lungu, H. van der Meiden, A. Hakola and P. Veis, Nucl. Mater. Energy, 2021, 27, 100990.
30. A. Semerok and C. Grisolia, Nucl. Instrum. Methods Phys. Res., Sect. A, 2013, 720, 31–35.
31. B. Schweer, G. Beyene, S. Brezinsek, N. Gierse, A. Huber, F. Irrek, V. Kotov, V. Philipps, U. Samm and M. Zlobinski, Phys. Scr., 2009, 138, 014008.
32. H. J. van der Meiden, S. Almaviva, J. Butikova, V. Dwivedi, P. Gasior, W. Gromelski, A. Hakola, X. Jiang, I. Jogi, J. Karhunen, M. Kubkowska, M. Laan, G. Maddaluno, A. Marín-Roldan, P. Paris, K. Piip, M. Pisařcík, G. Sergienko, M. Veis, P. Veis and S. Brezinsek, The EURO fusion WP PFC team, Nucl. Fusion, 2021, 61, 125001.
33. D. Gallot-Duval, C. Quere, E. De Vito and J. B. Sirven, Spectrochim. Acta, Part B, 2024, 215, 106920.
34. L. Y. Sun, D. Wu, C. Li, J. Wu, S. H. Hong, E. Bang, Z. H. Hu, F. Ding, G. N. Luo and H. B. Ding, Nucl. Mater. Energy, 2022, 31, 101174.
35. J. M. Liu, D. Wu, D. Y. Zhao, S. M. Liu, X. H. Hu, C. Li, L. Z. Cai and H. B. Ding, Fusion Eng. Des., 2023, 195, 113930.
36. B. T. Manard, H. B. Andrews, C. D. Quarles, V. C. Bradley, P. Doyle, N. A. Zirakparvar, D. R. Dunlap and C. R. Hexel, J. Anal. At. Spectrom., 2023, 38, 1412–1420.
37. A. Favre, V. Morel, A. Bultel, G. Godard, S. Idlahcen, M. Diez, C. Grisolia and F. Perry, Opt. Laser Technol., 2022, 150, 107913.
38. M. Imran, L. Y. Sun, P. Liu, H. Sattar, D. Y. Zhao, Z. Mu and H. B. Ding, Surf. Interface Anal., 2019, 51, 210–218.
39. C. Li, J. Oelmann, S. Brezinsek, M. Rasinski, C. P. Dhard, R. Konig, Y. F. Liang, H. B. Ding, C. Linsmeier and W. X. Team, Spectrochim. Acta, Part B, 2019, 160, 105689.
40. S. M. Liu, C. Li, H. C. Wu, L. F. Li, J. M. Liu, D. Wu, R. Hai and H. B. Ding, Spectrochim. Acta, Part B, 2023, 209, 106783.
41. NIST Atomic Spectra Database (ver.5.11), National Institute of Standards and Technology,  DOI:10.18434/T4W30F.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ja00208c

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