# Quantification of Aluminum Gallium Arsenide (AlGaAs) Wafer Plasma Using Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS)

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## Abstract

**:**

^{17}cm

^{−3}. It is further observed that the plasma parameters including electron temperature and electron number density have an increasing trend with laser irradiance and a decreasing trend along the plume length up to 2 mm. Finally, the elemental concentrations in terms of weight percentage using the CF-LIBS method were calculated to be Ga: 94%, Al: 4.77% and As: 1.23% for sample-1; Ga: 95.63%, Al: 1.15% and As: 3.22% for sample-2; and Ga: 97.32%, Al: 0.69% and As: 1.99% for sample-3. The certified concentrations were Ga: 95%, Al: 3% and As: 2% for sample-1; Ga: 96.05%, Al: 1% and As: 2.95% for sample-2; and Ga: 97.32%, Al: 0.69% and As: 1.99% for sample-3. The concentrations measured by CF-LIBS showed good agreement with the certified values reported by the manufacturer. These findings suggest that the CF-LIBS technique opens up an avenue for the industrial application of LIBS, where quantitative/qualitative analysis of the material is highly desirable.

## 1. Introduction

## 2. Experimental Setup

## 3. Material

## 4. Results and Discussions

#### 4.1. LIBS Emission Studies

^{2}5s

^{2}S

_{1/2}→3d

^{10}4s

^{2}4p

^{2}P

_{1/2}transition, and 417.20 nm due to 4s

^{2}5s

^{2}S

_{1/2}→3d

^{10}4s

^{2}4p

^{2}P

_{3/2}transition, followed by singly ionized arsenide (As I) and singly ionized aluminum (Al I) lines. The identification of the spectral lines belonging to various elements was accomplished using the National Institute of Standard and Technology (NIST) database [28]. The detected major and minor emission lines of sample-1, along with their wavelengths, transition configuration, transition probabilities, and upper level energies, are presented in Table 2. These optical emission lines are used to estimate the concentrations of the elements Ga, As, and Al. For the quantitative analysis of the AlGaAs samples, plasma parameters, such as plasma temperature and electron number density, were calculated by assuming that the plasma is optically thin and in local thermodynamic equilibrium (LTE).

#### 4.2. Plasma Temperature (T_{e})

_{e}) and electron density (N

_{e}). Several methods and techniques for determining the plasma temperature and number density have been utilized in previous LIBS studies [18,29,30]. However, in the present work, we used the Boltzmann plot method for measuring the plasma temperature. By assuming that the plasma population is obeying the Boltzmann distribution, we used the following Boltzmann equation to construct the Boltzmann plots [31,32]:

_{ij}is the spectral line intensity of the transition j→i, $\lambda $ is the transition wavelength, h is the Planks constant, A is the transition probability, ${g}_{i}$ is the statistical weight of the upper level, c is the velocity of light, ${E}_{i}$ is the energy of the upper level, $k$ is the Boltzmann constant, T

_{e}is the excitation temperature, ${N}_{e}$ is the total number density, and $P\left(T\right)$ is the partition function. To draw the Boltzmann plot, we have selected the optically thin emission lines of Ga I, As I, and Al I that are free from self-absorption and also follow the local thermodynamical equilibrium (LTE). The constructed Boltzmann plots for Ga I, As I, and Al I are presented in Figure 3, displaying excellent linearity (R

^{2}~0.999). The plasma temperatures have been obtained from the slopes (1/kT

_{e}) of the linear fit. The calculated plasma temperatures for Ga, As, and Al are (5730 ± 500 K), (5675 ± 500 K), and (5827 ± 500 K), respectively. The selected emission lines and their atomic parameters were taken from the NIST database and are listed in Table 2. The errors in the calculated plasma temperatures mainly come from the uncertainties present in the reported transition probabilities and the measurement of the line intensities. For the quantitative analysis, we have used a mean value of the plasma temperature, (5744 ± 500 K).

#### 4.3. Plasma Electron Number Density (N_{e})

_{e}) was calculated from the full width at half maximum (FWHM) of the Stark-broadened line profile of the neutral gallium (Ga I) at 417.20 nm [34,35].

_{r}is the reference electron number density, which is ${10}^{16}{\mathrm{cm}}^{-3}$ for the neutral line. A Voigt fitting profile (Cauchy–Lorentz distribution and a Gaussian distribution) of the Ga I emission line at 417.20 nm, which takes into account the instrumental resolution $\left(~0.06\mathrm{nm}\right)$ and the Doppler width $\left(~0.0036\mathrm{nm}\right)$, is shown in Figure 4. The electron number density is determined as: $\left(7.06\pm 0.1\right)\times {10}^{17}{\mathrm{cm}}^{-3}$.

#### 4.4. Local Thermodynamical Equilibrium (LTE)

#### 4.5. Laser Irradiance and Spatial Dependence on the Plasma Parameters

^{17}cm

^{−3}to 7.25 × 10

^{17}cm

^{−3}, respectively. The increase in electron temperature and electron number density happens due to high laser irradiance, which generates a higher number of free electrons and hot plasma. Furthermore, the increasing trend in electron temperature and electron number density occurs because plasma formation and laser absorption take place simultaneously [38].

## 5. Chemical Composition by CF-LIBS

_{k}(eV) is the energy of the upper level, T is the excitation temperature (eV), and k

_{B}is the Boltzmann constant. All the atomic factors used for the analysis were taken from the NIST database [28]. The concentrations (${W}^{\gamma}$) of the neutral atoms in the sample are calculated using Equation (4). To calculate the concentration of the ionized species, the Saha–Boltzmann equation was used [29,30,33,35]:

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Optical emission spectrum of the AlGaAs sample covering the wavelength range from 200 nm to 670 nm.

**Figure 3.**Typical Boltzmann plots for sample-1 using several neutral emission lines of Ga, As, and Al.

**Figure 4.**A typical Stark-broadened line profile of Ga I at 417.20 nm along with the Voigt fitting profile.

**Figure 5.**Variation in the electron temperature and the electron number density for Ga as a function of laser irradiance.

**Figure 6.**Variation in the electron temperature and the electron number density for Ga as a function of distance.

**Figure 7.**A histogram across elements versus concentration with varying wt.% of Al, Ga and As for both certified and CF–LIBS. (

**a**–

**c**) bar chart shows the comparison of concentration calculated by the CF-LIBS technique with that of the certified in the three samples specifically S–1, S–2, and S–3.

Species | Sample-1 | Sample-2 | Sample-3 |
---|---|---|---|

Aluminium (Al) | 3.0 | 1.00 | 0.69 |

Gallium (Ga) | 95.0 | 96.05 | 97.32 |

Arsenide (As) | 2.0 | 2.95 | 1.99 |

$\sum Wt.\%$ | 100 | 100 | 100 |

Wavelength (nm) | Electron Configuration Transition Upper Level to Lower Level | Upper Level Energy/E_{k}(cm ^{−1}) | Transition Probability (s ^{−1}) |
---|---|---|---|

Gallium (Ga I) | |||

Ga I 233.82 | 6d ^{2}D_{5/2}→4p ^{2}P_{3/2} | 43,580.44 | $9.75\times {10}^{6}$ |

Ga I 237.12 | 7s ^{2}S_{1/2}→4p ^{2}P_{1/2} | 42,158.77 | $5.57\times {10}^{6}$ |

Ga I 241.86 | 7s ^{2}S_{1/2}→4p ^{2}P_{3/2} | 42,158.77 | $1.00\times {10}^{7}$ |

Ga I 245.00 | 5d ^{2}D_{3}_{/2}→4p ^{2}P_{3/2} | 40,802.86 | $2.87\times {10}^{7}$ |

Ga I 250.01 | 5d ^{2}D_{5/2}→4p ^{2}P_{3/2} | 40,811.41 | $3.34\times {10}^{7}$ |

Ga I 265.98 * | 6s ^{2}S_{1/2}→4p ^{2}P_{1/2} | 37,584.77 | $2.44\times {10}^{7}$ |

Ga I 271.96 * | 6s ^{2}S_{1/2}→4p ^{2}P_{3/2} | 37,584.77 | $4.68\times {10}^{7}$ |

Ga I 287.40 * | 4d ^{2}D_{3/2}→4p ^{2}P_{1/2} | 34,781.66 | $4.68\times {10}^{8}$ |

Ga I 294.36 * | 4d ^{2}D_{5/2}→4p ^{2}P_{3/2} | 34,787.85 | $8.04\times {10}^{8}$ |

Ga I 403.20 * | 5s ^{2}S_{1/2}→4p ^{2}P_{1/2} | 24,788.53 | $9.70\times {10}^{7}$ |

Ga I 417.20 * | 5s ^{2}S_{1/2}→4p ^{2}P_{3/2} | 24,788.53 | $1.89\times {10}^{8}$ |

Ga I 639.60 | 6p ^{2}P_{3/2}→5s ^{2}S_{1/2} | 40,417.62 | |

Ga I 641.30 | 6p ^{2}P_{1/2}→6p ^{2}S_{1/2} | 40,376.45 | |

Arsenide (As I) | |||

As I 228.81 * | 5s ^{2}P_{3/2}→4p^{3} ^{2}D_{5/2} | 54,605.30 | $1.1\times {10}^{9}$ |

As I 234.98 * | 5s ^{2}P_{1}_{/2}→4p^{3 2}D_{3/2} | 53,135.60 | $6.8\times {10}^{8}$ |

As I 274.49 * | 5s ^{2}P_{3/2}→4p^{3 2}P_{1/2} | 54,605.30 | $1.0\times {10}^{8}$ |

As I 278.02 * | 5s ^{2}P_{3/2}→4p^{3 2}P_{3/2} | 54,605.30 | $3.1\times {10}^{8}$ |

As I 286.04 * | 5s ^{2}P_{1/2}→4p^{3 2}P_{1/2} | 53,135.60 | $1.1\times {10}^{8}$ |

Aluminium (Al I) | |||

Al I 308.20 * | 3d ^{2}D_{3/2}→3p ^{2}P_{1/2} | 32,435.45 | $2.35\times {10}^{8}$ |

Al I 309.30 * | 3d ^{2}D_{5/2}→3p ^{2}P_{3/2} | 32,436.79 | $4.37\times {10}^{8}$ |

Al I 394.40 * | 4s ^{2}S_{1/2}→3p ^{2}P_{1/2} | 25,347.75 | $9.98\times {10}^{7}$ |

Al I 396.15 * | 4s ^{2}S_{1/2}→3p ^{2}P_{3/2} | 25,347.75 | $1.97\times {10}^{8}$ |

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**MDPI and ACS Style**

Alrebdi, T.A.; Fayyaz, A.; Asghar, H.; Zaman, A.; Asghar, M.; Alkallas, F.H.; Hussain, A.; Iqbal, J.; Khan, W. Quantification of Aluminum Gallium Arsenide (AlGaAs) Wafer Plasma Using Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS). *Molecules* **2022**, *27*, 3754.
https://doi.org/10.3390/molecules27123754

**AMA Style**

Alrebdi TA, Fayyaz A, Asghar H, Zaman A, Asghar M, Alkallas FH, Hussain A, Iqbal J, Khan W. Quantification of Aluminum Gallium Arsenide (AlGaAs) Wafer Plasma Using Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS). *Molecules*. 2022; 27(12):3754.
https://doi.org/10.3390/molecules27123754

**Chicago/Turabian Style**

Alrebdi, Tahani A., Amir Fayyaz, Haroon Asghar, Asif Zaman, Mamoon Asghar, Fatemah H. Alkallas, Atif Hussain, Javed Iqbal, and Wilayat Khan. 2022. "Quantification of Aluminum Gallium Arsenide (AlGaAs) Wafer Plasma Using Calibration-Free Laser-Induced Breakdown Spectroscopy (CF-LIBS)" *Molecules* 27, no. 12: 3754.
https://doi.org/10.3390/molecules27123754