Calibration Free Laser Induced Breakdown Spectroscopy of

i

Hira Shakeel

2019

Department of Physics and Applied Mathematics

Pakistan Institute of Engineering and Applied Sciences

Nilore, Islamabad, Pakistan

Calibration Free Laser Induced Breakdown

Spectroscopy of Silicon, Germanium and their

Alloys

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Reviewers and Examiners

Foreign Reviewers

1. Prof. Dr. Jin YU

2. Dr. Tariq Hasan Gilani

3. Dr. Massimo F. Bertino

Thesis Examiners

1. Prof. Dr. Aslam Baig

2. Dr. Shahid Ali

3. Dr. Muhammad Nawaz

Head of the Department (Name): ___Dr. Muhammad Yousaf Hamza____

Signature with Date: _________________________________

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Certificate of Approval

This is to certify that research work presented in this thesis titled “Calibration free laser

induced Breakdown Spectroscopy of silicon, germanium and their alloys” was conducted by

Ms. Hira Shakeel under the supervision of Dr. Sami ul Haq.

No part of this thesis has been submitted anywhere else for any other degree. This thesis is

submitted to Department of Physics and Applied Mathematics in partial fulfillment of the

requirements for the degree of Doctor of Philosophy in the field of Physics.

Student Name: Hira Shakeel Signature:----------------------------

Examination Committee:

Examiners Name, Designation & Address Signature

Internal Examiner 1

Internal Examiner 2

Internal Examiner 3

Supervisor Dr. Sami ul Haq, PS, NILOP, Islamabad.

Co-Supervisor Dr. Masroor Ikram, CS, PIEAS, Islamabad.

Department Head Dr. Muhammad Yousaf Hamza, DCE,

PIEAS, Islamabad.

Dean Research PIEAS Prof. Dr. Naeem Iqbal, DCE, PIEAS,

Islamabad.

i

Thesis Submission Approval

This is to certify that the work contained in this thesis entitled “Calibration free laser induced

Breakdown Spectroscopy of silicon, germanium and their alloys”, was carried out by Hira

Shakeel and in my opinion, it is fully adequate, in scope and quality, for the degree of Ph.D.

Furthermore, it is hereby approved for submission for review and thesis defense.

Supervisor: _____________________

Name: Dr. Sami ul Haq

Date:

Place: NILOP, Islamabad.

Co-Supervisor: __________________

Name: Dr. Masroor Ikram

Date:

Place: PIEAS, Islamabad.

Head, Department of Physics and Applied Mathematics: ___________________

Name: Dr. M. Yousaf Hamza

Date:

Place: PIEAS, Islamabad.

i

Hira Shakeel

Submitted in partial fulfillment of the requirements

for the degree of Ph.D.

2019

Department of Physics and Applied Mathematics

Pakistan Institute of Engineering and Applied Sciences

Nilore, Islamabad, Pakistan

Calibration Free Laser Induced Breakdown

Spectroscopy of Silicon, Germanium and their

Alloys

ii

Dedication

To

My Loving Parents

iii

Author’s Declaration

I Hira Shakeel hereby declare that my PhD Thesis Titled “Calibration free laser induced

Breakdown Spectroscopy of silicon, germanium and their alloys” is my own work and has

not been submitted previously by me or anybody else for taking any degree from Pakistan

Institute of Engineering and Applied Sciences (PIEAS) or any other university/institute in the

country/world.

At any time if my statement is found to be incorrect (even after my graduation), the university

has the right to withdraw my PhD degree.

_____________

(Hira Shakeel)

Date:

PIEAS, Islamabad.

iv

Plagiarism Undertaking

I Hira Shakeel solemnly declare that research work presented in the thesis titled “Calibration

free laser induced Breakdown Spectroscopy of silicon, germanium and their alloys” is

solely my research work with no significant contribution from any other person. Small

contribution/help wherever taken has been duly acknowledged or referred and that complete

thesis has been written by me.

I understand the zero tolerance policy of the HEC and Pakistan Institute of Engineering and

Applied Sciences (PIEAS) towards plagiarism. Therefore, I as an author of the thesis titled above

declare that no portion of my thesis has been plagiarized and any material used as reference is

properly referred/cited.

I undertake that if I am found guilty of any formal plagiarism in the thesis titled above even after

the award of my PhD degree, PIEAS reserves the rights to withdraw/revoke my PhD degree and

that HEC and PIEAS has the right to publish my name on the HEC/PIEAS Website on which

name of students are placed who submitted plagiarized thesis.

_____________

(Hira Shakeel)

Date:

PIEAS, Islamabad.

v

Copyrights Statement

The entire contents of this thesis entitled “Calibration free laser induced Breakdown

Spectroscopy of silicon, germanium and their alloys” by Hira Shakeel are an intellectual

property of Pakistan Institute of Engineering and Applied Sciences (PIEAS). No portion of the

thesis should be reproduced without obtaining explicit permission from PIEAS.

vi

Table of Contents

Dedication ........................................................................................................................... ii

Author’s Declaration .......................................................................................................... iii

Plagiarism Undertaking ..................................................................................................... iv

Copyrights Statement .......................................................................................................... v

Table of Contents ............................................................................................................... vi

List of Tables ...................................................................................................................... x

Abstract .............................................................................................................................. xi

List of Publications ........................................................................................................... xii

List of Abbreviations ....................................................................................................... xiii

Acknowledgement ........................................................................................................... xiv

Introduction to LIBS ..................................................................................................... 1 1

1.1 Laser Induced Breakdown Spectroscopy (LIBS) .................................................. 1

1.2 Laser Induced Plasma............................................................................................ 1

1.3 Local Thermodynamic Equilibrium (LTE) ........................................................... 3

1.4 Stoichiometric Ablation ........................................................................................ 5

1.5 Plasma Opacity ...................................................................................................... 5

1.6 Self-Absorption ..................................................................................................... 6

1.7 Determination of Plasma Temperature ................................................................. 8

1.7.1 Boltzmann Plot Method ..................................................................................... 8

1.7.2 Saha Boltzmann Plot Method .......................................................................... 10

1.8 Electron Number Density .................................................................................... 11

1.9 Quantitative Analysis using LIBS ....................................................................... 14

1.9.1 Calibration Free LIBS (CF-LIBS) Technique ................................................. 14

1.9.2 Variants of Calibration Free LIBS................................................................... 16

1.10 LIBS Configurations ........................................................................................... 17

1.10.1 Single Pulse LIBS ............................................................................................ 17

1.10.2 Double Pulse LIBS .......................................................................................... 18

1.11 Layout.................................................................................................................. 21

Instrumentation and Experimental Procedure ............................................................. 22 2

2.1 Laser System ....................................................................................................... 22

2.2 Spectrometer........................................................................................................ 23

vii

2.3 Spectrometer Calibration..................................................................................... 25

2.4 Sample Chamber ................................................................................................. 27

2.5 Optical Systems ................................................................................................... 28

2.6 Optimization of Experimental Parameters .......................................................... 29

2.7 Spectral Data Analysis ........................................................................................ 30

2.8 Experimental Procedure ...................................................................................... 31

2.8.1 Single Pulse LIBS Setup.................................................................................. 31

2.8.2 Double Pulse LIBS Setup ................................................................................ 32

Spectroscopic Characterization of Laser Induced Plasma .......................................... 34 3

3.1 Introduction ......................................................................................................... 34

3.2 Experimental Arrangement ................................................................................. 35

3.3 Results and Discussion ........................................................................................ 35

3.3.1 The Emission Spectra ...................................................................................... 35

3.3.2 Laser Irradiance Dependence of Plasma Parameters ....................................... 39

3.3.3 Spatial Dependence of Plasma Parameters ...................................................... 43

3.3.4 Pressure Dependence of Plasma Parameters ................................................... 44

Calibration Free Laser Induced Breakdown Spectroscopy of Al-Si Alloy ................. 48 4

4.1 Introduction ......................................................................................................... 48

4.2 Experimental Details ........................................................................................... 50


4.3.1 Optimization of the Experimental Parameters................................................. 50

4.3.2 Analysis of the Emission Spectra .................................................................... 51

4.3.3 Self-Absorption Correction in Emission Spectra ............................................ 54

4.3.4 Quantitative Analysis of Al-Si Alloy .............................................................. 56

Double Pulse Calibration-Free LIBS: Quantitative Analysis of Ge/Si Alloys and Solar 5

Cells ............................................................................................................................ 62

5.1 Introduction ......................................................................................................... 62

5.2 Experimental Setup ............................................................................................. 64


5.3.1 Effect of Inter-Pulse Delay and Energy Ratio on the Emission Spectra ......... 65

5.3.2 Analysis of LIBS Spectra ................................................................................ 67

5.3.3 Plasma Temperature and Electron Number Density ....................................... 69

5.3.4 Elemental Concentration of Ge Alloys ............................................................ 73

Conclusion and Future Plan ........................................................................................ 79 6

7 References……………………………………………………………………………80

viii

List of Figures

Figure 1-1: Temporal evaluation of laser induced plasma emissions. ............................................ 2

Figure 1-2: Temporal evaluation of laser induced plasma emissions. ............................................ 3

Figure 1-3: Boltzmann plot obtained neutral emission lines. ......................................................... 9

Figure 1-4: Stark broadened line profile of Hα line. ..................................................................... 12

Figure 1-5: (a) Collinear dual-pulse arrangement, (b) Orthogonal reheating configuration (c)

Orthogonal pre-ablation spark. .................................................................................. 20

Figure 2-1: Energy level diagram of the triply ionized Nd ion. .................................................... 23

Figure 2-2: Schematic of Czerny-Turner spectrometer. ............................................................... 24

Figure 2-3: Emission Spectra of low pressure Hg-Ar standard lamp. .......................................... 25

Figure 2-4: (a) Intensity profile of Standard lamp and (b) Spectrometer calibration curve. ........ 27

Figure 2-5: (a,b) Photographic view, schematic diagram of LIBS Sample chamber under

controlled atmosphere and (c) in ambient air. ............................................................ 27

Figure 2-6: Pictorial view of beam combiner assembly. This assembly combines two laser beams

collinearly................................................................................................................... 28

Figure 2-7: Emission spectra analyzed using Matlab code. ......................................................... 30

Figure 2-8: Schematic diagram of single pulse LIBS arrangement. ............................................. 32

Figure 2-9: Schematic diagram of dual pulse LIBS in collinear configuration. ........................... 33

Figure 3-1: Portion of the emission spectra generated by 1064 nm laser, showing the spectral

lines used in this study. The inset shows an expanded view of the multiplet of

spectral lines at 252 nm. ............................................................................................. 36

Figure 3-2: Variation of emission intensities of the selected silicon lines, acquired through 1064

nm laser ablation, with (a) laser irradiance, (b) distance from the target surface and

(c) with ambient pressure. .......................................................................................... 38

Figure 3-3: Boltzmann plot for the determination of electron temperature using neutral silicon

emission lines yield the electron temperature as 7000 ± 500 K at 11.4 GWcm-2

irradiance of 1064 nm laser wavelength. ................................................................... 40

Figure 3-4: Variation of electron temperature of Si plasma, as a function of laser irradiance from

2 to 16 GWcm-2

of 1064 nm and 532 nm of Nd: YAG laser. .................................... 41

Figure 3-5: Variation in the electron number density of Si plasma as a function of laser

irradiance. ................................................................................................................... 42

Figure 3-6: Spatial distribution of the electron temperature of Si plasma. ................................... 43

Figure 3-7: Spatial distribution of the electron number density Si plasma................................... 44

Figure 3-8: Variation of electron temperature of Si plasma with ambient pressure from 45 to 550

mbar at fixed irradiance of 1064 and 532 nm of Nd: YAG laser. .............................. 45

Figure 3-9: Variation of electron number density of Si plasma with ambient pressure from 45 to

550 mbar at fixed irradiance of 1064 and 532 nm of Nd: YAG laser. ....................... 46

Figure 4-1: Portion of the single pulse LIBS spectra of Al-Si alloy, acquired at a laser irradiance

of 15.7 GWcm-2

of 1064 nm of the Nd: YAG laser. .................................................. 52

file:///C:/Users/pieas/Downloads/final%20thesis%2025.9.2018%20evening.docx%23_Toc525714348








ix

Figure 4-2: The upper trace is the original spectra whereas the lower trace is the background

subtracted spectra of the Al-Si alloy. ......................................................................... 53

Figure 4-3: Saha Boltzmann plot using Ti lines with and without self-absorption correction in

integrated intensities. ................................................................................................. 56

Figure 4-4: Boltzmann plots of the species in the alloy without self-absorption correction. ....... 57

Figure 4-5: Boltzmann plots of the species in the alloy with self-absorption correction. ............ 58

Figure 4-6: Boltzmann plots of the ionized species in alloy without self-absorption correction. 59

Figure 4-7: Boltzmann plots of the ionized species in alloy with self-absorption correction. ..... 59

Figure 4-8: Elemental concentration of all the elements in alloy, except Al and Si..................... 60

Figure 5-1: Emission intensities as a function of (a) inter-pulse delay and (b) laser energy ratio.

The vertical lines indicate optimized values of inter-pulse delay at 1.6 μs and 1:3

energy ratios, respectively. ......................................................................................... 66

Figure 5-2: Portion of the double and single pulse emission spectra, recorded at 40 mJ total laser

energy. The arrows represent the emission lines detected only in double pulse spectra. ............. 68

Figure 5-3: The upper trace is the emission spectra recorded with collinear double pulse

arrangement at 10 +30 mJ laser energies, whereas the lower spectra is single pulse

spectra with same total energy of 40 mJ. ................................................................... 69

Figure 5-4: Saha-Boltzmann plot obtained from Cu I and Cu II emission lines in collinear double

pulse configuration with 1.6 µs inter-pulse delay and 10 +30 mJ laser pulse energies.

.................................................................................................................................... 70

Figure 5-5: Boltzmann plots of neutral and ionized emission lines of the species present in Ge-

Cu/Si alloy. The solid lines are the linear fitting over the experimental data points. 71

Figure 5-6: Boltzmann plots of the emission lines of Gd, Ge, Si, present in alloy and (b-d) show

the Boltzmann plots, built using Si emission lines of three solar cells. ..................... 72

Figure 5-7: Concentration of the elements present in Ge-Cu/Si and Ge-Ba/Si alloy. The graph in

the inset represents the concentration of trace elements in parts per million. ........... 75







x

List of Tables

Table 3-1: Spectroscopic data of silicon emission lines used for determination of electron

temperature................................................................................................................. 39

Table 4-1: List of the selected emission lines used for self-absorption evaluations and Boltzmann

plots. The wavelengths highlighted in bold are internal reference lines. ................... 55

Table 4-2: Compositional analysis of Al-Si alloy with and without self-absorption correction in

the emission intensities. ............................................................................................. 61

Table 5-1: Elemental composition of the germanium-based alloys.............................................. 75

Table 5-2: Elemental concentration determined using Calibration Free LIBS with and without

Boltzmann plots. ........................................................................................................ 77

Table 5-3: Elemental composition determined using Calibration Free LIBS without constructing

Boltzmann plots. ........................................................................................................ 78

xi

Abstract

The present research work describes the compositional analysis of silicon, germanium and their

alloys using calibration free laser induced breakdown spectroscopy (CF-LIBS) technique. In the

initial experimental work, the fundamental plasma parameters of silicon have been studied as a

function of laser irradiance, ambient pressure, and distance along the plume length using the

fundamental (1064 nm) and second harmonic (532 nm) of Q-switched Nd: YAG laser were

investigated. Electron temperature was determined using Boltzmann plot method and electron

number density by the Stark broadening in the line profile.

In the next series of experiments, calibration free laser induced breakdown spectroscopy (CF-

LIBS) technique has been applied for the quantitative analysis of silicon and germanium alloys

and polycrystalline solar cells. The emission spectrum of a standard Al-Si alloy was captured

using single pulse LIBS and the analysis confirmed the presence of Mg, Al, Si, Ti, Mn, Fe, Ni,

Cu, Zn, Sn, and Pb in the alloy. After background subtraction and incorporating self-absorption

corrections, the corrected emission intensities and accurate evaluation of plasma temperature

(10100 K) yield the reliable quantitative results up to a maximum 2.2% deviation from the

standard values. Furthermore, the double-pulse LIBS in collinear configuration was used to

record the emission spectra of two unknown alloys (Ge-Cu/Si, Ge-Ba/Si), a standard alloy (Gd-

Ge-Si) and three polycrystalline solar cell samples. The experimental parameters such as inter-

pulse delay, gate delay and energy ratio between the two laser pulses were optimized to improve

the signal to background and signal to noise ratio in the LIBS spectra. The concentration of the

species was determined with and without using Boltzmann plots. The later approach was used

for the trace elements with emission lines not enough to draw Boltzmann plot of it. The results of

this approach show maximum deviation of 4% from the reference data. Furthermore, the analysis

of unknown polycrystalline silicon solar cells extracted the concentration of trace impurities C,

Ca, Sb, In, Sn, Ti, Al, and K in parts per million (ppm). These impurities in crystalline structure

reduce the conversion efficiency of solar cells and therefore their detection and quantification is

important for efficient photovoltaic applications.

xii

List of Publications

1. Hira Shakeel, S.U. Haq, Qamar Abbas, Ali Nadeem, V. Palleschi, “Quantitative analysis

of Ge/Si alloys using double-pulse calibration-free laser-induced breakdown

spectroscopy”, Spectrochimica Acta Part B 146 (2018) 101-105.

2. Hira Shakeel, S. U. Haq, Ghulam Aisha, Ali Nadeem , “Quantitative analysis of Al-Si

alloy using calibration free laser induced breakdown spectroscopy (CF-LIBS)”, Phys. of

Plasmas 24 (2017) 02463516.

3. Hira Shakeel, Saboohi Arshad, S. U. Haq, and Ali Nadeem, “Electron temperature and

density measurements of laser induced germanium plasma”, Phys. of Plasmas 23 (2016)

053504.

4. Hira Shakeel, M Mumtaz, S Shahzada, A Nadeem and S. U. Haq, “Spectroscopic

characterization of laser ablated silicon plasma”, Plasma Sources Science and

Technology 23 (2014) 035006.

5. Hira Shakeel, S. U. Haq, Qamar Abbas and Ali Nadeem, “Double-pulse Calibration-free

Laser-induced Breakdown Spectroscopy: A step towards quantitative real time analysis",

Appl. Spectrosc. (2019) Submitted.

6. G. Aisha, M. Shah, Shaista Shahzada, S.U. Haq, H. Shakeel, Ali Nadeem, “Investigation

of the 4snf 1F3 Rydberg states of zinc and determination of the dipole polarizability of

the Zn+ ion”, Spectrochimica Acta Part B 142 (2018) 85–90.

7. S. U. Haq, L. Ahmat, M. Mumtaz, Hira Shakeel, S. Mahmood and A. Nadeem,

“Spectroscopic studies of magnesium plasma produced by fundamental and second

harmonics of Nd:YAG laser”, Phys. of Plasmas 22, (2015) 083504.

* Publications 1-5 are included in the thesis.

xiii

List of Abbreviations

AES Atomic Emission Spectroscopy

CCD Charged Coupled Device

CF Calibration Free

DP Double Pulse

FWHM Full Width at Half Maximum

LIBS Laser Induced Breakdown Spectroscopy

LTE Local Thermodynamic Equilibrium

Nd:YAG Neodymium Yttrium Aluminum Garnet

Ne Electron Number Density

PPM Parts Per Million

RSD Relative Standard Deviation

SNR Signal-to-Noise Ratio

SP Single Pulse

xiv

Acknowledgement

All the praises for Almighty ALLAH, who enabled me to initiate, continue and complete the

research work successfully. I would like to express my sincere gratitude to my advisor, Dr.

Sami-ul-Haq for giving me the opportunity to join their group and gave access to the

research facilities in Laser Spectroscopy laboratory NILOP. I am grateful for his continuous

support at every stage of this research, right from beginning to the end. It has been an honor

for me to be his first PhD student. I am also thankful to my co-supervisor, Dr. Masroor Ikram

for all his suggestions during my course work and crucial days of qualifying examination at

PIEAS. My sincere thanks also go to Dr. Ali Nadeem for his professional valuable guidance

throughout my research work particularly during thesis write-up. I would like to thank my

thesis defense committee: Prof. Dr. Muhammad. Aslam Baig, Dr. Muhammad Nawaz, and

Dr. Shahid Ali for their insightful comments and encouragement, but also for the hard

questions which incented me to widen my research from various perspectives. I also owe my

thanks to Dr. Victor Contreras of UNM, Mexico for providing the computer code for the

analysis of emission spectra as well as for the calibration free calculations. I am especially

grateful to my beloved husband Mr. Osama Ahmed Rana and his head Mr. Nasir Mahmood

from Optics Lab for providing me germanium alloy sample.

I thank my fellow lab mates Mr. Qamar Abbas and Amir Israr for the stimulating discussions

and support during the experiments. I enjoyed a lot during my studies at PIEAS due to some

very good friends for our memorable sudden trips and gossips.

I am also thankful to my parents, husband and siblings who provided me through moral and

emotional support in all my pursuits. Finally, I would like to thank my loving daughter

Zainab for the cute things to make me laugh during the stressful time.

1

Chapter 1

Introduction to LIBS 1

1.1 Laser Induced Breakdown Spectroscopy (LIBS)

Laser Induced Breakdown Spectroscopy (LIBS) is the most promising elemental analysis

technique for solids, liquids and gaseous samples, additionally; it requires little or no sample

preparation. Therefore, LIBS has been used in wide variety of applications with reasonable

accuracy such as elemental analysis [1-4], energy field [5], biological sciences [6, 7], nuclear

industry [8], and in environmental sciences [9, 10]. LIBS involves a high energy laser pulse

focused on the sample surface, as a result, it produces a plasma plume due to rapid melting or

vaporization. The plasma depends on the laser parameters such as irradiance, pulse duration,

wavelength as well as on the interaction volume, nature of a target and ambient environment.

The supersonic expansion of plasma normal to the sample surface produces shock waves and

compresses the ambient air. Consequently, energy is transferred to the surrounding atmosphere

via radiative transfer, thermal conduction, and shock waves. The atomic emission from LIBS

plasma is used to identify sample constituents, their quantitative analyses and for the

determination of plasma temperature. Normally, LIBS data are recorded by directing the plasma

emissions on the entrance slit of broadband high-resolution spectrometer. Moreover, it has been

observed that the plasma parameters such as plasma temperature, electron number density,

radiative transfer, and plasma velocity are strongly dependent on the nature of plasma.

1.2 Laser Induced Plasma

Shortly after the invention of laser in 1960s, the laser induced plasma was produced and reported

[11, 12], which consist of neutrals species, ions, electrons and clusters. LIBS plasma is

characterized as weakly ionized plasma with the ratio of electrons to other species is typically

less than 10%. From the temporal behavior of a LIBS plasma (See Fig. 1-1), it is obvious

Chapter 1: Introduction to LIBS

2

that in the early stage of plasma, the ionization and continuum emissions are dominant. But at

later stage, the electron-ion recombination takes place; atoms recombine to form molecules, and

the background continuum decays quickly with time. It is evident from the figure that after a few

microseconds of plasma ignition, the spectral emission lines start to appear. Therefore, most of

the emission spectra in LIBS are recorded after hundreds of nanoseconds to few microseconds of

the plasma generation.

Fig. (1-2) shows possible transitions occurring during the plasma cooling time. At the

early stage plasma, the continuum emission is dominant due to bremsstrahlung (free–free

transitions) and electron ion recombination (free–bound) events.

0μss Continuum emission, < 𝟏𝟎𝟎𝒏𝒔

Ionic emission, 𝟏𝟎𝟎𝒏𝒔~𝟓𝝁𝒔

Atomic emission, 5𝟎𝟎𝒏𝒔~𝟐𝟎𝝁𝒔

Molecular bands emission, 5~𝟓𝟎𝝁𝒔

1μs 10μs

Molecular bands

Atomic emission

Ionic emission

Continuum emission

Laser pulse

Gate delay Gate width

Figure 1-1: Temporal evaluation of laser induced plasma emissions.


3

In recombination process, a free electron is bound into an atomic or ionic energy level and

releases maximum amount of its kinetic energy, whereas in Bremsstrahlung phenomenon light

emission is due to the deceleration of electrons during collisions. At a later stage, the bound-

bound transitions (line radiation) and molecular band such as CN or C2 may appear in the LIBS

spectra. Among all these emissions, the most important radiations are the line emissions, which

originate due to bound-bound transitions of atoms or ions.

When the sufficiently intense laser (e.g. femtosecond pulse ~ 1013 W/cm2) interacts with a

metallic target, the conduction band electrons absorb laser photons through inverse

bremsstrahlung mechanism. Whereas, in case of semiconductors, when the photon energy is

greater than the band gap, electrons excited to the conduction band result an increase in the

population in the conduction band. But when the photon energy is less than band gap, multi-

photon absorption causes population growth in the conduction band [13].

1.3 Local Thermodynamic Equilibrium (LTE)

Local thermodynamic equilibrium, commonly abbreviated as LTE, is a state of plasma in which

the collisional excitation and de-excitation are dominant over the radiative processes. In LTE, the

Figure 1-2: Temporal evaluation of laser induced plasma emissions.


4

probability of de-excitation from an excited state through inelastic collision should be large

compared to the spontaneous emission, which is possible at high plasma densities. The minimum

requirement of this assumption is determined by the electron number density eN , which is

defamed by the following McWhirter criterion: [14, 15]

332/114104.1 cmETN ee (1-1)

Where Ne (cm-3

) represents the electron number density, ∆E (eV) is the energy difference

between the upper and lower energy levels and Te is the plasma temperature in eV. Since the

McWhirter criterion is derived for stationary homogenous plasmas, therefore this condition is

necessary but not sufficient for plasma to fulfill LTE. In laser induced breakdown spectroscopy

(LIBS), the existence of local thermodynamic equilibrium (LTE) is essentially required,

therefore, Cristoforetti et al. [16] reported a detailed study on LTE beyond the McWhirter

criterion. They proposed another criterion for the existence of LTE, in which the relaxation time

of the plasma, i.e., the time needed to establish the excitation and ionization equilibrium, is much

shorter than the time required for the variation of thermodynamic parameters. Griem and Drawin

[17, 18] described that among all the processes involving the ground state, the coefficient of

collisional excitation to the first excited state of the resonance series is the lowest and can

therefore be considered for an estimation of relaxation time ( ) as follows.

kT

EkTE

gfn

ji

ji

ije

relax exp103.6 21

4

, (1-2)

As mentioned earlier, LTE plasmas can be characterized by the same temperature,

therefore, the excitation temperature which determines the population of the atomic and ionic

levels should be similar to the ionization temperature, which controls the distribution of atoms of

the same element among different ionization states.

Laser induced plasma also show spatial gradients in temperature and electron number

density due to the dissipation of heat at the plasma edges via conduction and radiative processes.

These gradients may disturb the plasma LTE, therefore, Cristoferetti et al. [16], proposed a


5

criterion in which the diffusion length of atoms or ions (during the relaxation time) must be

shorter than the variation length of temperature and electron number density in the plasma as:

kT

E

gfM

E

gfn

lji

ijA

ji

ije

diff2

exp104.1

21

12

(1-3)

Where 3cmne is the electron density, ijf (dimensionless) is the oscillator strength, jiE

(eV) is the energy difference of the participating levels,

g is the effective Gaunt factor and kT

(eV) is the plasma temperature.

1.4 Stoichiometric Ablation

Laser ablation is a nonlinear process in which laser interacts with the sample, resulting mass

removal and plasma formation. Laser induced plasma consists of excited species, neutral atoms,

electrons, ions, molecules, particles and clusters. In stoichiometric condition, the chemical

composition of the plasma must be the representative of the sample constituents. Therefore,

understanding of laser-material interaction is very important to achieve the condition of

stoichiometric ablation and to produce plasma at optimized experimental conditions for best

LIBS performance. In 1991, Chan and Russo [19] reported for the first time that stoichiometric

ablation can only be achieved at high power density 109 W/ cm

2. These high powers can be

easily achieved with a pulsed laser. Subsequently, Russo and co-workers [20] reported further

understanding of the phenomenon along with detailed explanation of the processes which result

in the establishment of stoichiometric ablation. As calibration-free technique accounts for all

species present in a sample, therefore, stoichiometric ablation is the pre-requisite for the

quantitative analysis.

1.5 Plasma Opacity

The laser induced plasma is optically thin when all the emitted photons escape out of the plasma,

without being scattered or re-absorbed. The radiation emitted out of plasma is governed by the

following expression:


6

L

eI

(exp1

)(

)()( ,

(1-4)

The parameters e , and L are the emissivity, absorption coefficient and plasma length,

respectively. For small values of , the condition for optically thin plasma is achieved:

LeL

eI

(

)(

)()( . (1-5)

The optical thickness of the plasma can be checked by inspecting the emission spectra.

When the observed relative intensities of the spectral lines do not follow intensity selection rules

and the strong emission lines saturate, the plasma is said to be optically thick. The resonance

lines will effectively saturate and become flat-topped indicating self-absorption. In extreme

cases, emission lines are observed with a dip at the central frequency; this is due to the self-

reversed effect.

1.6 Self-Absorption

In LIBS, the emission line intensities are used to determine sample composition,

therefore, one must be confident that the plasma is optically thin i.e. the radiation emitted is not

reabsorbed along the optical path length of the plasma volume. However, when the plasma

density is high enough, the plasma emissions are reabsorbed in the plasma volume. This

absorption distorts the emission profile and the phenomenon is referred as self-absorption. It is

more dominant in resonance lines, but weak transitions may suffer from self-absorption. The

effect of self-absorption is to reduce the peak intensity and increase the full width at half

maximum (FWHM) of the emission line profile, resulting flat topped line profile or in extreme

case dip is appeared in the line center.

The evaluation and correction of self-absorption in the emission line profile is necessary for the

accurate determination of plasma parameters and compositional analysis. Consequently many

experimental and theoretical procedures are introduced for the self-absorption correction in LIBS

spectra [21-24]. However, in the present work, we have used the self-absorption correction

technique reported by Sun and Yu [25]. In this method, an internal reference line for each species

with lower transition probability and higher excitation energy is used to extract the self-


7

absorption coefficient from the ratio with the line to be corrected for self-absorption. The

measured line integral intensity with self-absorption is given by the following relation;

kT

Ee

TU

gAFCfI i

S

i

ijS

bij

, (1-6)

Where ijI is the line integrated intensity, bf is the coefficient of self-absorption, F is a

constant representing the optical efficiency of the system, SC is the species concentration, ijA is

the transition probability for the given line, ig is the level degeneracy, TUS is the partition

function for the emitting species, iE represents the energy of the upper state, k is the Boltzmann

constant and T is the plasma temperature. The limiting value of bf is between 0 and 1, 0bf

means the spectral line is extremely self-absorbed, whereas the value 1 shows that the spectral

line is not affected by self-absorption. As self-absorption is weak for the emission lines with low

transition probabilities and higher excitation energies, therefore considering the intensity ratios

of other emission lines to an internal reference line yield the self-absorption coefficient as

follows;

kT

EEe

gA

gA

I

I

f

f im

iij

mmn

mn

ij

b

R

b

, (1-7)

Where the subscripts R represent the internal reference and m and i are the upper and

lower states of reference transition. Assuming negligible self-absorption in reference line b

Rf , the

self-absorption in any other line of the same species can be evaluated as;

kT

EEe

gA

gA

I

If im

iij

mmn

mn

R

ijb

, (1-8)

To eliminate the self-absorption in the integrated intensity of the emission line under

consideration, the observed integrated intensity is divided by the above self-absorption

coefficient.

kT

EEe

gA

gAI

f

II im

mmn

iij

mn

R

b

ijij

corr

. (1-9)

The corrected integrated intensities can now be used in Boltzmann, Saha Boltzmann plots

and in the compositional analysis using both the calibration curve and in the calibration free

LIBS procedure.


8

1.7 Determination of Plasma Temperature

The spectroscopic determination of plasma electron temperature is carried out using the absolute

or relative emission intensities such as line pair ratio or Boltzmann plot, and the ratio of line to

continuum intensity, etc. provided that the local thermodynamic equilibrium conditions must

satisfy in small measurement volume. In the following sections, two commonly used methods for

the estimation of plasma temperature are described.

1.7.1 Boltzmann Plot Method

The most widely used spectroscopic technique for the determination of plasma electron

temperature is the Boltzmann plot method. The relative emission intensities of atomic or ionic

lines corresponding to each species can be used to evaluate the electron temperature provided the

main contribution to the excitation and de-excitation mechanisms comes from electron impact.

Assuming the local thermodynamic equilibrium is established within the plasma, the population

in the excited states follows the Boltzmann distribution [26] , as given by the following

expression:

kT

EE

g

g

N

N 12

2

1

1

2 exp , (1-10)

Here N1 and N2 represent the level population densities and rest of the parameters is the

same as described earlier. Using Eq. (1-9), the total number density N of the species can be

expressed as follows;

3210 NNNNN

...2

21

10

0

0

kT

Eg

kT

Egg

g

NN , (1-11)

Where 0N represent the ground state population density and 0g is the statistical weight.

Rearranging the above equation yield the following expression;

TUg

N

kT

Eg

g

NN

K

KK

0

0

00

0 exp

, (1-12)

Partition function TU is stated as follows;


9

0exp

K

KK

kT

EgTU , (1-13)

Hence the population of level is given as follows;

kT

Eg

TU

NN K

KK exp , (1-14)

The relative population of the energy levels is given as;

kT

EE

g

g

N

N iK

i

K

i

K exp (1-15)

The emission line radiant intensity (W/sr), incorporating the number density and the

transition probability A is expressed as [27] ;

kT

EUgAhcNI exp40 , (1-16)

UhcNE

kTgAI 4ln

1ln 0 , (1-17)

39000 42000 45000 48000 51000 54000

-12.5

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

ln(

g)

Eupper state

(cm-1

)

Slope = -2.058x10-4

Te = 7000 K

Figure 1-3: Boltzmann plot obtained from neutral emission lines.


10

Eq. (1-17) is a linear equation with slope kT1 , which is used to extract the plasma temperature.

A typical Boltzmann plot as illustrated in Fig. (1-3), is built using gAIln versus upper state

energy. Since many emission lines from the same ionization state of a species are used in

Boltzmann plot, therefore, it gives reliable plasma temperature. The key factors that need to be

considered are accurate values of emission line intensities as well as reliable spectroscopic data

of the emission lines used in the plot.

1.7.2 Saha Boltzmann Plot Method

The Saha Boltzmann plot method produces more accurate plasma temperature due to the use of

spectral lines from different ionization stages [28-31]. As the emission lines corresponds to both

neutral and ionic species, a combination of Boltzmann excitation and Saha ionization

distributions are used to get Saha Boltzmann plot with extend the range of energies.

kT

EE

h

mkT

TU

TU

N

Nn zz

z

z

z

z

e112/3

211exp

2

)(

)(2 , (1-18)

Where 3cmne is the electron number density, 3cmN Z and 31 cmN Z

are the

number densities of any two consecutive ionization stages. The parameters gm , 1zE and

1 zE are the electron mass, the first ionization potential and correction in the ionization

potential respectively [32]. The expressions for the Saha–Boltzmann plot method is given by the

following equation. [27, 32, 33].

tQhcNkT

E

gA

IZ

j

Z

j

Z

ji

ji

Z

ji lnln

, (1-19)

Where

e

Z

j

Z

ji

ji

Z

ji

Z

j

Z

ji

ji

Z

ji

n

T

h

mkz

gA

I

gA

I 2323

2

22lnlnln

,

(1-20)

and

1

0

Z

K

KKZ

j

Z

j EEEE . (1-21)


11

In this expression, Z represents the ionization stage, i.e. 0Z correspond to bound

stage, whereas 1Z represents the first ionization stage. In Eq. (1-19), the correction term

varies as 23ln T , which is slowly varying compared to T1 term. Therefore, the temperature is

obtained using an iterative procedure, for which the initial value of temperature is obtained from

Boltzmann plot method. A new value of temperature is obtained which is plugged in again to get

new value of plasma temperature. This iterative procedure continues until temperature

converges.

The use of emission lines from different ion stages of the same species increases the

energy spread between the levels when compared with the Boltzmann plot. Consequently, the

slope obtained by a linear regression is less affected from measurement noise, which results

accurate plasma temperature. Moreover, the electron number density can now be determined

from the intercept [34].

1.8 Electron Number Density

The spectroscopic technique which is used for the determination of electron number density is

the Stark broadening in the emission line profile. As the line profile is the consequence of many

broadening effects such as Doppler, pressure and instrumental etc., nevertheless the main

contribution comes from the Stark effect [35]. The Stark broadening is due to the coulomb

interactions between the emitter atoms and the charged particles in the plasma. Therefore the

Stark broadening of an isolated line is a useful parameter for determination of the electron

number density, provided the Stark broadening parameter is known. The full width at half

maximum (FWHM) of a Stark broadened line profile can be expressed as [36-38];

163

14

1

1616

2

110

2.1110

5.310

2 eD

ee NN

NA

N , (1-22)

Where nm and nmA are the electron and ion impact parameters, the values can be

found in the literature [39]. 3cmNe and 3

cmND are the electron and particle density in

Debye sphere. As the ions are much heavier than electrons, the ionic contribution can therefore

be neglected and the above equation is modified as follows;


12

16

2

110

2 eN . (1-23)

The FWHM of the emission line must be non-self-absorbed and free from instrumental

broadening. Sherbini et al. [40] proposed the use of H line (656.28 nm), which is least self-

absorbed due to very small concentration in air but present in almost every emission spectrum

recorded in ambient environment. Moreover, in case of linear Stark effect, the broadening is

more, causing less relative uncertainty and hence reliable electron number density, which can be

extracted as follow [41, 42];

2

3

21,

TCHNe

, (1-24)

And

2

3

21

21

121002.8

HNe. (1-25

Figure 1-4: Stark broadened line profile of Hα line.


13

The FWHM

21 is obtained by fitting Voigt function over the line profile as shown in

Fig. (1-4) and the coefficient TC , is reported in Griem [39], whereas, the empirical

coefficient 2

1 can be obtained in ref [43].

Two different approaches are used for the instrumental function. In the first approach both

Stark and instrumental broadening are considered Lorentzian and therefore both are subtracted

linearly as follows;

instmeasStark

In the second approach, the instrumental broadening is described by a Gaussian profile,

which is subtracted in quadrature from the measured profile to get Stark broadened line profile.

The approximated formula which connects the width of a Voigt profile to its

Lorentzian and Gaussian components is:

22

42G

LL

In our case, the Gaussian width is given by the instrumental broadening, if, as it should,

1

L

G

and, consequently

L we can further approximate the previous expression

obtaining:

2

22

L

GLL

i.e.

222

GLL

And

22

a instrkSt (1-26)


14

1.9 Quantitative Analysis using LIBS

The two most common LIBS methods for the quantitative analysis are calibration curve and

calibration free methods. In calibration curve method, the reference samples are used and

calibration curves are constructed between the emission intensity and the known concentration

using reference samples. The concentration of unknown sample can be determined by fitting

emission intensity on the standard calibration curves. This method requires the matrix matched

standard samples which in most cases are not available.

1.9.1 Calibration Free LIBS (CF-LIBS) Technique

The calibration free LIBS (CF-LIBS) technique has been extensively used for the

quantitative analysis, after its introduction in 1999 by Ciucci et al. [44]. The standard-less LIBS

technique has lots of potential applications for the quantitative analysis in research and industry,

therefore, the analysis of alloys, coal, soil, geological and biological samples etc. are reported in

literature [45-47]. This method is based on the fundamental assumptions of plasma being

homogeneous and satisfy LTE conditions, the spectral lines are optically thin and the

stoichiometric condition must be fulfilled [48, 49].

For the LTE plasma, the population of an excited level can be related to the total

concentration of neutral atoms or ions using the Boltzmann relation. According to the Boltzmann

relation the measured emission line intensity is represented using the following relation:

kTE

eS

S eTU

gFCI

, (1-27)

Here I is the line integrated intensity, the experimental factor F describes the optical

efficiency of the setup, SC is the species concentration, eS TU is the partition function, E is the

upper state energy of a transition, eT represents the plasma temperature which must be same

under LTE assumption and BK is the Boltzmann constant. The values of F , eT and SC are

determined from the experimental data.

By taking the logarithm of Eq. (1-27), we obtain


15

eS

S

e

j

jji

ji

TU

FC

kT

E

gA

Ilnln , (1-28)

Rearranging the above equation in linear form:

Sqmxy ,

Where

jji

ji

gA

Iy ln , jEx ,

ekTm

1 ,

eS

SS

TU

FCq ln

Similar expressions can be defined for each plasma species. The integrated intensity for

each transition is represented as a point in the Boltzmann plot. Under LTE assumption, all plots

will give same value of slope (m) but different intercepts ( Sq ). The experimental factor F can be

evaluated using normalization condition.

S

SC 1

S

q

e

II

S

q

e

I

S

IIS

IS eTUeTUF , (1-29)

Where I

Sq and II

Sq are the intercepts from the Boltzmann plot and e

I

S TU , e

II

S TU are the

partition functions of neutral and singly ionized species respectively. The partition function is

calculated as;

i

kTE

ieSeegTU ,

After determination of plasma electron temperature, the elemental concentration can be

obtained using the following expression;

F

eTUeTUC

IIS

IS q

e

II

S

q

e

I

SS

. (1-30)


16

However, in some particular situations, the emission spectrum exhibits lines that

correspond to only single species of a certain element. In such cases, to include the contribution

of ionic species in overall elemental concentrations, the Saha equation can be used [27] which

relates the concentrations of species with successive ionization states of same element.

kT

EE

h

kT

TU

TU

N

Nn zz

z

z

z

z

e

112/3

211exp

2

)(

)(2 . (1-31)

The electron density en is extracted using Stark broadening in the line profile. Otherwise,

the electron density can also be measured through the Saha equation itself, if the concentration

ratio of two successive ionization stages has been evaluated for at least one element. In principle,

the information regarding just one element is enough for the complete evaluation of the species

concentration because the electron density will be same for all the elements like plasma

temperature. However, for more precise results the contribution of more spectral lines can be

used to average out the effects of the uncertainties on the transition probabilities.

1.9.2 Variants of Calibration Free LIBS

Since 1999, when Ciucci for the first time proposed and implemented the calibration free

analysis technique, many variants of this technique are reported in literature. Initially, efforts

have been made to correct self-absorption issues in the emission spectra. Many resonance lines

from the major elements often suspect for self-absorption were excluded from the analyses. In its

new formulation, Bulajic et al. [21] implemented a self-absorption correction scheme in the CF-

LIBS technique via curve of growth (COG) method. The recursive algorithm calculates the

density of species using input parameters, evaluates self-absorption, and recalculates the

densities. Sun and Yu [25] proposed a self-absorption correction procedure in the emission lines

and improved the accuracy of CF-LIBS results. Recently Pisa group published a comprehensive

discussion on three variants of calibration free technique, namely one-point calibration,

calibration free inverse method and C-sigma approach [50]. They concluded that one-point-

calibration method is the most appropriate against self-absorption and matrix effect. Burakov et

al. [45] proposed a variant in which known concentration of one of the basic components is used

to correct all other components of the sample. De Giacomo et al. [51] proposed self-calibrated


17

LIBS (SC-LIBS) approach, in which they relaxed the LTE condition to some extent and instead

internal normalization was achieved using plasma continuum emission and neutral species. In

subsequent years, Wang et al. [52] used the internal standard concentration for the determination

of number density of rest of the sample constituents. In literature, some variants are reported,

which are not directly the variants of CF-LIBS, however, improve the accuracy of this technique.

For example, Aguilera et al.[53] used Saha–Boltzmann plot for the determination of plasma

temperature and relative number densities of the elements from the corresponding intercepts,

which is more accurate than Boltzmann plot method.

In the present work, we have used the internal reference method [23, 25] to quantify and

eliminate the self-absorption in the selected emission lines. Typically, the trace elements in a

sample appear with few emission lines which are not sufficient to build Boltzmann plot and get

intercept, but their contribution to overall elemental concentration should be incorporated. In

order to overcome this issue, we have used the variant of CF-LIBS, proposed by Diaz Pace et al.

[54], according to which the plasma temperature is estimated using the emission lines of any one

element and the intercepts for the rest of species is determined using the modified form of Eq. (1-

27).

eS

S

e

j

jji

ji

TU

FC

kT

E

gA

Ilnln .

(1-32)

1.10 LIBS Configurations

1.10.1 Single Pulse LIBS

The unusual advantages of LIBS, including lack of sample pre-treatment, small measurement

times, and the ability of real-time multi-element detection tempt the researchers to focus their

efforts to establish new techniques for reliable LIBS-based quantitative analysis. These

advantages make the LIBS technique preferable over other conventional analytical techniques

such as inductively coupled plasma optical emission spectroscopy (ICP-OES), inductively

coupled plasma mass spectroscopy (ICP-MS), and atomic absorption spectroscopy (AAS) [55].

In LIBS, conventionally single pulse is used to produce plasma on the sample surface, the

associated optical emissions are analyzed for the determination of plasma parameters,


18

compositional analysis and other applications. LIBS is a powerful analytical tool in closed

contact and standoff arrangement. The performance of single pulse LIBS depends on the laser

pulse energy, laser wavelength, pulse duration of the laser and the time delay between plasma

formation and spectral acquisition. Many groups investigated the dependence of plasma on these

laser parameters and experimental conditions. Now LIBS has been successfully demonstrated for

a quick qualitative sample analysis. In the SP-LIBS, a few micro-grams of the sample is required

to produce plasma, therefore, it can be termed as a non-destructive technique [56]. Due to non-

destructive feature, the technique finds its applications in the analysis of precious samples like

antique artifacts [57]. In subsequent years, single pulse LIBS has been applied for the

quantitative analyses of metallic alloys [2, 58], non-metallic alloys [45], and soil samples [59,

60]. The key feature about LIBS is its great analytical capability to carry online, in-situ and

remote analysis of the samples placed in harsh, inaccessible, and contaminated environment.

Despite the above mentioned capabilities, the conventional single pulse technique suffers

from significant matrix effects and high background signals [35]. SP-LIBS also undergo shot-to-

shot signal fluctuations. The main factors contributing the fluctuations in the measurements are

the variations in plasma temperature and coupling of laser energy with the target surface [56].

Moreover low sensitivity and relatively poor limits of detection ppm) are the main drawbacks

of SP-LIBS when compared with other analytical techniques [61, 62].

1.10.2 Double Pulse LIBS

Various strategies are adopted to increase the sensitivity and accuracy of LIBS technique [63-

66]. These studies were aimed to investigate the use of multiple pulses on different samples and

matrices [67-71] and reported enhanced emission line intensities and improved signal to

background ratio [72]. Irradiating second pulse to the plasma, results in enhanced sensitivity due

to various factors, such as re-excitation, increased mass ablation and reduced plasma shielding of

the incident laser beams. In this configuration, it is possible to improve the analytical capabilities

without dropping the LIBS features [67]. Evtushenko et al. [73, 74] were the first to investigate

laser induced spectra in air using two synchronised lasers. Subsequently, Piepmeier and

Malmstadt [75] and Scott and Strasheim [76] studied the laser absorption in plasma of aluminum

alloy and examined many laser plasma plumes as a spectrochemical source for quantitative


19

analysis. In double pulse LIBS (DP-LIBS), the signal enhancement depends on the target

material, laser pulse energies, inter pulse delay, combination of pulses with different

wavelengths [67, 77] and geometrical configurations of the laser beams [78-80]. Cremers et al.

[81] in 1984 and several other groups performed double pulse LIBS experiments in various

configurations, such as collinear, orthogonal, and parallel geometry [82-88].

Fig. (1-5) illustrates the schematics of collinear and orthogonal beam geometries for double pulse

LIBS. The arrows represent the direction of laser beam propagation and the labeling on these

arrows show their temporal sequence. Fig. (1-5a) refers to collinear geometry, in which the first

laser produces plasma, whereas the suitably delayed second laser interacts with the plasma

produced by the first laser. Consequently, an increased sample ablation, more plasma volume,

enhanced collisions and more hot plasma is produced as compared to single pulse with same

total energy for both lasers [89]. Cremers et al. [81], for the first time used orthogonal and

collinear beam geometries on aqueous solution and observed that collinear geometry yield

maximum signal enhancement. In orthogonal reheating arrangement as shown in Fig. (1-5b), the

first laser pulse directed perpendicular to the sample resulting in plasma generation, whereas, the

second delayed pulse travelling parallel to the sample surface re-heats the plasma. In this

configuration, the signal enhancement is due to energy absorption in the plasma during the re-

heating pulse. Gonzalez et al. [90] proposed that in the re-heating arrangement second pulse

causes an efficient increase in emitting species due to the vaporization induced from the first

pulse.

In case of orthogonal pre-ablation case [91], the first laser pulse travelling parallel to the

sample surface rarefying the ambient air in front of sample depicted as shown in Fig. (1-5c). The

second delayed pulse hits the sample surface orthogonally and produces plasma. Sanginés. et al.

[92] employed the orthogonal DP-LIBS in reheating and pre-ablative configurations at different

inter-pulse delays. For both schemes, the signal enhancement was achieved when compared with

corresponding SP-LIBS.


20

Figure 1-5: (a) Collinear dual-pulse arrangement, (b) Orthogonal reheating

configuration (c) Orthogonal pre-ablation spark.

(a)

2

1

(b) (c)

1

2

1

2 1

2


21

1.11 Layout

In this research project we applied the calibration-free LIBS for the quantitative analysis of

silicon and germanium alloys. The first chapter deals with the brief description of the theoretical

background of laser induced plasma, plasma temperature, number density, and the core topic of

the research calibration free LIBS technique using single and double pulse configurations. The

second chapter describes the details of the instruments used in the experiments and the

experimental procedure both for single and double pulse LIBS.

Chapter three is based on the detail investigation of plasma parameters of silicon, their

dependence on the laser irradiance, laser wavelength, distance from the target surface, ambient

pressure. This chapter also has brief overview of the same studies on germanium target. In

chapter four, the quantitative analysis of the standard aluminum-silicon alloy is presented. The

plasma was produced using the fundamental harmonic (1064 nm) of the Nd: YAG laser. The

self-absorption corrected emission spectra have been used for the qualitative and quantitative

analyses.

In chapter five, the research work was further extended to the quantitative analysis of two

unknown alloys (Ge-Cu/Si and Ge-Ba/Si) using double pulse calibration free LIBS technique.

The plasma was produced using two collinear Nd: YAG lasers, operating at 1064 nm. The

experimental parameters were optimized to maximize the signal to background ratio.

Stoichiometric ratio of Ge-Cu/Si and Ge-Ba/Si alloys is first determined using double pulse

technique. Further, the quantitative analysis of standard Gd-Ge-Si alloy was performed using

variant of double pulse calibration free LIBS technique. In this variant the Boltzmann plot for

one species was built for plasma temperature and the concentration of all the elements were

determined without Boltzmann plots. In addition, three polycrystalline silicon solar cells were

investigated that yields the concentration of silicon as 99.78, 98.09 and 99.45% respectively, and

trace impurities were detected in parts per million (ppm). The impurities in crystalline structure

reduce the conversion efficiency of solar cells and therefore their detection and quantification is

important for efficient photovoltaic applications.

22

Chapter 2

Instrumentation and Experimental Procedure 2

The research work presented in this thesis, was performed using Q-switched Nd: YAG laser

systems, LIBS sample chamber, optical components, and high resolution broadband

spectrometer. In the following sections, all the apparatus has been described in detail.

2.1 Laser System

The commonly used laser in majority of LIBS experiments is the Q-switched Nd:YAG laser

system, which is a flash lamp pumped with pulse duration in the range between 6–10 ns. It is a

four level solid state laser that emits light in the infrared region (1064 nm) of the spectrum.

Furthermore, by frequency doubling and mixing the second (532 nm) and third (355 nm)

harmonics are produced. A small number of Yttrium ions (Y3+

), 0.2 to 1.4% are replaced by the

Neodymium (Nd3+

) ions in the active medium of Nd:YAG crystal. The active media is in the

shape of a cylindrical rod, pumped by flash lamps and placed inside a highly reflecting optical

cavity. The electronic energy levels of the Nd3+

ions in the lasing medium excited to the higher

energy states (4F5/2,

2H9/2 and

4F3/2) as shown in the energy level diagram in Fig. (2-1). After a

lifetime of the state the electrons in the higher energy states decay non-radiatively to the

metastable 4F3/2 state, laying at 11502 cm

-1. Stimulated emission results in the radiative transfer

of Nd3+

ions from 4F3/2 energy state to

4I11/2 (positioned 2000 cm

-1). As a result, light is emitted at

1064 nm wavelength. Due to shorter lifetime of state 4I11/2 (10 ns) compared with the upper state

4F3/2 (250 μs), negligible number of atoms reside in the lower state.

High powers can be obtained using Q-switched operation with moderate pulse energies.

For this, an electro-optic Q-switch shutter is placed inside the cavity to avoid photons to

complete the whole path through the cavity and induce stimulated emission. Thus, the population

inversion can be attained between the upper and lower levels. By an appropriate

Chapter 2: Instrumentation and Experimental Procedure

23

timed gate pulse, the Q-switch is triggered allowing photons to make many traverses of the laser

cavity and results in a high-power short duration laser pulse.

In the present work, we used a Q-switched Nd:YAG laser (Brilliant from Quantel) with a

pulse duration of 6 ns and repetition rate of 10 Hz to perform single pulse LIBS experiments.

The pulse to pulse fluctuations in the output pulse energy was less than 5%, which is appreciable

for the laser induced plasma experiments where accuracy and precision are much required. In

dual pulse LIBS (DP-LIBS) experiments, laser pulses from two different lasers were used to

produce and re-heat the plasma in collinear configuration. The lasers were operating at

fundamental wavelength of 1064 nm for both SP-LIBS and DP-LIBS experiments.

2.2 Spectrometer

The diagram of Czerny–Turner spectrometer is shown in Fig. (2-2). In the present experimental

work we have used a HR2000+ Czerny–Turner spectrometer in which the plasma emissions are

4

H9/2

2

H9/2

4

F5/2

4

F3/2

4

I11/2

2000

0 1800

0

1150

2

600

0

200

0

400

0

Pump Band

Non radiative

decay

Upper

level

Laser

action 1064 nm

Lower

level

Ground level

Optical

Pumpin

g

Figure 2-1: Energy level diagram of the triply ionized Nd ion.

En

erg

y (

cm

-1)


24

Figure 2-2: Schematic of Czerny-Turner spectrometer.

imaged onto the entrance slit and reach the first mirror that collimates the light and direct it onto

the grating. Light dispersed at different angles strikes a mirror that focuses the light on the

detector array in the form of a spectrum. The fundamental grating equation is described as

follows:

,sinsin nd

(2-1)

Where d is the grating period, is the angle of incidence, is the diffraction angle, n is

diffraction order, and is the wavelength of the incident light. The linear dispersion can be

expressed as;

,cos

nf

d

dx

d

(2-2)

Here x is the coordinate in the detector plane and f is the focal length of the exit mirror.

The CCD detector has 1024×1024 pixels. The resolving power of a spectrometer is given as;

,NnR

(2-3)

In the above expression n is the diffraction order and N is the total number of grooves on

the grating irradiated by the light and is the spectral separation of the two emission lines. The

resolving power depends on the wavelength and increases with the spectral order but

independent of the size and spacing of the grating. However, different ruling are used in

spectrometer depending on the wavelength.


25

.

# D

ff

(2-4)

Here, D and f are the diameter and focal length of the mirror respectively from the

entrance slit to the first mirror. The resolution of the spectrometer can be improved by increasing

the number of grooves in grating but at the expense of the spectral range. Furthermore, the

resolution also depends on entrance slit, and again this is done at the cost of the signal strength.

2.3 Spectrometer Calibration

The wavelength and spectral response calibration of a spectrometer is necessary to validate the

recorded spectrum. The calibration of a spectrometer is the basis of quantitative applications of

the emission spectra. To assign a spectral line to a particular element, the recorded emission

spectrum must have wavelengths with certain accuracy. The wavelength calibration uses a

standard lamp such as a “Hg-Ar low pressure lamp”. The Hg-Ar lamp provides good spectral

coverage for different regions of the LIBS emission spectrum.

Figure 2-3: Emission Spectra of low pressure Hg-Ar standard lamp.


26

The following third order polynomial expression is used, which relates the pixel number with

wavelength from the NIST atomic database [93].

3

3

2

21 pCpCpCIp (2-5)

Where p is the wavelength at pixel p, I is the wavelength at 0 pixel and C1, C2, C3 are the

first, second and third coefficients (nm/pixel) respectively. The emission spectrum of Hg-Ar

lamp as depicted from Fig. 2-3 was recorded with suitable integration time and the pixel no. and

corresponding wavelength from literature was tabulated. The square and cube of the pixel

number were calculated to find out C2, and C3 coefficients. The spread sheet program (Excel,

Microsoft) used to perform the linear regression analysis yield all the three coefficients and

intercept. The R-squared values in the outcome of regression analysis must be close to unity,

indicating the best regression analysis. In the spectrometer setting, the values of coefficients

were updated and the procedure was repeated for each channel.

Each component in LIBS setup, particularly the spectrometer has a certain spectral

response, which depends on the wavelength. Moreover, the detector used to record the emitted

light has a response function that varies with wavelength. In order to radiometrically calibrate the

LIBS setup, standard intensity lamps are used, which require re-calibration after their lifetime

[94].

In the present work, the intensity calibration of LIBS spectrometer was performed using

Deuterium Tungsten-Halogen Calibration Light Source (DH-2000-CAL, Mikropack GmbH,

Germany), covering the spectral range from UV to NIR. The operating software Spectra Suite

(Ocean Optics, Inc.) was used with step by step procedure for intensity calibration. During the

calibration, the intensity of lamp was used to calibrate the spectrometer. Fig. (2-4a) illustrate the

intensity profile of the lamp, whereas Fig. (2-4b) represents the intensity profile obtained through

spectrometer that is well overlapped over the intensity profile of the lamp. The exact overlapping

shows that the spectrometer is calibrated against the emission spectra of the lamp.


27

Figure 2-4: (a) Intensity profile of Standard lamp and (b) Spectrometer calibration curve.

2.4 Sample Chamber

A stainless steel vacuum chamber was prepared for the investigation of plasma parameters at

different ambient pressure. The photographic view and the schematic diagram of the vacuum

chamber is shown in Fig. 2-5(a, b). The chamber consists of four ports, for connecting vacuum

pumps, for inserting fiber for emission light collection, for laser beam delivery and one for

mechanical feed- through for target rotational and translational motion, maintaining the vacuum

so that plasma is formed on fresh surface.

Figure 2-5: (a, b) Photographic view, schematic diagram of LIBS sample chamber under

controlled atmosphere and (c) in ambient air.

(c) (b) (a)

(a) (b)


28

The experimental work in ambient air was performed in a commercially available LIBS

sample chamber (Ocean Optics Inc.) as shown in Fig. (2-5c), using single pulse. The inside

platform can be manually controlled by x-y stage. The laser beam focusing lens and fiber probe

are mounted on the same railing, and can be adjusted easily.

2.5 Optical Systems

The beam delivery for LIBS with single and dual laser system is shown in Fig. (2-6).

Light pulse from the first laser with horizontal polarization passes through dielectric polarizer,

which is directed by mirror towards the output aperture. The beam from second laser passes

through half wave plate to rotate the linear polarization from horizontal to the vertical plane and

is reflected towards dielectric polarizer. Due to vertical polarization, the dielectric polarizer

reflects the light pulse towards the path of first laser. Finally, the laser pulses at the same output

aperture can then be used separately for single pulse LIBS or in combination for dual pulse

LIBS. The emission from the laser induced plasma is collected by lens and is focused onto an

optical fiber bundle consisting of seven fibers each with a diameter of 600 µm. The output end of

this fiber bundle delivers the plasma light to the entrance slit of a spectrometer.

Figure 2-6: Pictorial view of beam combiner assembly. This assembly combines two laser

beams collinearly.


29

2.6 Optimization of Experimental Parameters

For the quantitative measurements, the emission line intensities are directly related to the

absolute or relative concentration of a sample. Several parameters affect the precision of LIBS

measurements include laser energy, lens to sample distance (LTSD), gate delay time and the gate

width. At low laser fluence, usually, the strong emission lines of major species and resonance

transitions from the trace elements are detected, but weak emission lines are not detected. On the

other hand, at high laser irradiance the emission lines of major constituents get saturated and

strong continuum appears. To get LIBS spectra, a true representation of the sample and to avoid

saturating emission lines, the optimum laser irradiance was used in the present experiments. At

this irradiance, the trace elements were detected with good signal to noise (S/N) ratio and major

elements were identified with sharp transitions and were free from saturation. It was observed

that by varying gate delay the intensity of atomic emission lines and continuum background was

changed. Background emissions were prominent in the early stage of the plasma but its rate of

decay is much faster than the atomic emission lines. Continuum (Bremsstrahlung) depends on

the plasma temperature and decay faster. After the plasma expansion (lower temperature) the

emission line signal dominates due to the recombination of the charged species in the plasma.

Because of different decay rates of the emission lines and the background continuum it became

easy to get the optimized conditions by adjusting the time window of the detector. Similarly, any

small change in lens-to-sample-distance (LTSD) causes a significant change in the intensity of

the emission lines from the trace elements. Hence, for accurate and reproducible results, the

LTSD should be fixed. In the present experiments, this parameter was optimized by taking a

burn pattern at different positions close to sample surface and the lens was fixed at optimized

position. The spectral response of the spectrometer was corrected using intensity calibrated lamp.

The wavelength calibration was performed with a standard Hg-Ar lamp and through regression

analysis the coefficients were updated. Pulse energies were calibrated by Scientech thermopile

and monitored by directing a small fraction of the laser pulses to a photodiode coupled with a

digital oscilloscope. Under these optimized conditions, the emission spectra of alloys were

recorded for the qualitative and quantitative analysis.


30

2.7 Spectral Data Analysis

In the present setup, the Czerny Turner spectrometer was used to record the emission

spectrum, which can resolve closely spaced lines and elements were identified accurately.

Therefore, the assignment of spectral lines is performed by considering the following points. The

knowledge of the sample .i.e. the sample is known to have high concentrations for some of the

elements present in the sample. Secondly, after subtracting background from the line intensities

the relative intensities are compared to the intensities specified in the NIST atomic database.

Moreover, for elements having multiple observed emission lines, the correlation between

observed intensities of various lines and the relative line intensities listed in NIST database is

established to avoid incorrect line assignment. In the LIBS spectrum, we often observed neutrals

and singly ionized species. If two lines spectrally interfere each other and one belongs to a

neutral species and the other to ionized species, it is most likely that the observed line belongs to

neutral species [27]. The last strategy, we have used that many elements have several strong

emission lines and if one line is observed the other strong lines of the same element should also

appear in the spectrum. As an example, if the strong aluminum lines at 394.4 and 396.1 nm

appears, the lines at 308.2 and 309.3 nm should also be detected in the spectrum [27].

Based on the above criteria, and in collaboration with Victor Lura of CIO, Mexico, we developed

synthetic spectrum of neutral and singly ionized species of elements using wavelength and

relative intensities available at NIST database.

Figure 2-7: Emission spectra analyzed using Matlab code.


31

The synthetic spectrum of a species was generated by fitting each line to a Lorentzian

profile, since the dominant broadening in the line profile is Stark broadening which follow

Lorentzian function. In the Matlab package, the Lorentzian parameters were optimized to obtain

best Lorentzian fit over the experimental spectra as shown in Fig. (2-7). The comparison of

observed spectra with reference spectra was done with correlation coefficient technique [95].

2.8 Experimental Procedure

2.8.1 Single Pulse LIBS Setup

The experimental setup used for the single pulse LIBS experiments is shown in Fig. (2-8). The

ablation source was Nd: YAG laser operating at its fundamental wavelength of 1064 nm with 7

ns pulse and 10 Hz repetition rate. The laser was capable of delivering a maximum of 850 mJ per

pulse energy. The laser energy was monitored using a calibrated energy meter (Field Max II,

Coherent, USA) and 10% of the laser beam was diverted to the photodiode for online energy

monitoring. The laser beam was focused on the sample surface and the lens to sample distance

was adjusted for each experiment to get optimum emission spectra. Usually the focus is kept

inside sample surface to avoid air breakdown in front of the sample surface. The plasma

emission was collected and transmitted via optical fiber bundle to the entrance slit of a

spectrometer. A set of seven miniature spectrometers (LIBS2500+, Ocean Optics, USA) was

used in the present experiments, with overall spectral range of 200-900 nm and optical resolution

of 0.1 nm. A charged coupled device (CCD) detector is installed in LIBS2500+ system with a

fixed gate width of 2.1 ms. To improve the signal-to-noise ratio, the spectral data acquisition was

delayed using LIBS operating software (OOILIBS). The samples were pelletized of approx.1.5

cm diameter and 0.5 cm thickness and fixed on the rotational platform to provide a fresh surface

each time and avoid crater formation. The possible non-uniformities of the sample surface and

fluctuations in laser energy were minimized by taking average of ten spectra at 10 different

locations of the sample.


32

Figure 2-8: Schematic diagram of single pulse LIBS arrangement.

2.8.2 Double Pulse LIBS Setup

The dual pulse LIBS setup shown in Fig. (2-9) consists of two Q-switched Nd:YAG

lasers (Quantel Brilliant (10 ns pulse width, 1064 nm wavelength, 10 Hz rep. rate) was used for

the current LIBS system. The laser energies were monitored with calibrated energy meter (Field

Max II, Coherent, USA) and the maximum fluctuation in energy of each laser was < 3%. The

laser beams were combined collinearly using a half wave plate, a mirror and a dielectric

polarizer. The half wave plate was used to rotate the linear polarization of the first laser beam

and the dielectric polarizer was used to recombine the beams. The collinear laser pulses were

focused on the sample surface to produce and reheat the plasma. The analytical performance of

double pulse LIBS (DP-LIBS) can be improved by optimizing delay and energy ratio between

laser pulses. At the optimized inter pulse delay, the energy ratio of the laser pulses was plotted

while keeping the total energy fixed, which yield maximum signal enhancement at particular

energy ratio between the first and second laser. Under these optimized parameters, the plasma

emission was collected and displayed in the form of emission spectra. The rest of the procedure

is same as described in case of single pulse LIBS.


33

Laser 2

λ/2 plate

Laser 1

Dielectric polarizer

Mirror

Optical fiber

L

Sample

Spectrometer

Computer

Delay

Generator

Figure 2-9: Schematic diagram of dual pulse LIBS in collinear

configuration.

34

Chapter 3

Spectroscopic Characterization of Laser Induced 3

Plasma

3.1 Introduction

The dynamics of laser produced plasma with respect to the experimental conditions is of great

importance in understanding plasma dynamics and in setting up the experimental conditions for

optimum performance [96]. These conditions can best be evaluated by determining electron

temperature and number density. Silicon has important application as a solar cell and the

polycrystalline silicon ingot are directly used to grow single crystals for photovoltaic

applications. The interaction of laser with semiconductor material is a complex phenomenon and

many research papers and review articles are available on this topic [97-99]. The plasma

parameters of silicon are investigated by many groups exploiting different conditions, e.g. Liu et

al. [100] investigated the plasma parameters at the early stage of a plasma (<300 ns) at 2–80

GWcm−2

laser irradiance and observed fast increase in electron temperature, number density and

degree of ionization beyond 20 GWcm−2

. Milan and Laserna [31] characterized the silicon

plasma, spatially and temporally by estimating the electron temperatures from 6000 to 9000 K,

ionic temperatures from 12000 to 17000 K with irradiance from 0.2 to 45 GWcm−2

and electron

number density reported as ≈1018

cm−3

. Pledif and Andreif [101] reported the electron

temperature as 1.5 eV and number density 1018

cm−3

, using a nitrogen laser at 337.1 nm and

Samek et al. [102] investigated spatially and temporally the plasma produced by femtosecond

laser (775 nm, pulse duration of 170–200 fs). A more acute pulsed laser (Ti : sapphire, 100 fs

pulse duration) and Nd :YAG laser (266 nm, 3 ns pulse duration) were used to compare the

ablation efficiency via crater depth [103] and observed that fs-ablated crater was about twice as

Chapter 3: Spectroscopic Characterization of Laser Induced Plasma

35

deep as the ns-crater. Amal et al. [104] compared the plasmas of single and double pulses

produced on the surface of silicon (1 1 1). They also performed experiments at various pressure

values, but could not find any appreciable change in the electron temperature and number

density. However, the signal enhancement was observed at shorter inter-pulse delay in

comparison with single-pulse LIBS. Cowpe et al. [105] studied the temporal dynamics of silicon

plasma, produced at different values of ambient pressure and reported the electron temperature

and electron number density as 9000–21000 K and 2.79 × 1016–5.59 × 10

19 cm

−3 respectively.

3.2 Experimental Arrangement

The details of the experimental procedure to produce silicon plasma and to record the emission

spectra is described in chapter 2 and shown in Fig. (2-8). Here only the specific details of

experiment are presented. In order to produce silicon plasma, 30-200 mJ energy of the 1064 nm

of Nd: YAG laser was focused on the sample surface with a convex lens of 10 cm focal length.

The spot size at focus is approx. 300 µm which produce area of 7.1x10-4

cm2 on the sample

surface. The optical emissions were recorded using LIBS2000 spectrometer with 2.1 ms gate

width and 3.5µs detector gate delay.

The plasma parameters were investigated with laser irradiance from 9 to 33 GWcm-2

and

their spatial distribution was inferred from the emission spectra recorded at fixed laser irradiance

along the plume length up to 5 mm. In addition, the plasma parameters were also investigated at

different ambient pressure. A stainless steel vacuum chamber was fabricated having ports for

beam delivery, light collection, sample insertion and to connect with vacuum pump. All the ports

were sealed with quartz windows and the chamber was evacuated down to 10-3

mbar. The

ambient pressure inside chamber was varied in the range 8-250 mbar and the emission spectrum

of silicon was recorded.

3.3 Results and Discussion

3.3.1 The Emission Spectra

Emission spectrum of silicon shown in Fig. (3-1) was recorded using 1064 nm of a Nd: YAG

laser at 10 GWcm−2

laser irradiance. This portion of the spectra shows well-resolved silicon lines


36

Figure 3-1: Portion of the emission spectra generated by 1064 nm laser, showing the

spectral lines used in this study. The inset shows an expanded view of the multiplet of

spectral lines at 252 nm.

and a multiplet structure around 252 nm, as shown in the inset. The emission lines of the

spectrum were designated using LS coupling rules and the NIST atomic database [93]. The

intensity and the line profile of the emission lines were used to determine the plasma parameters.

The number density of the excited species is proportional to the line profile (FWHM) and its

distribution reflects the spatial evolution of the excited species, whereas the electron temperature

is either proportional to the intensity ratio of spectral lines or can be extracted from the plot of

integrated intensities of several lines (the Boltzmann plot method).

Fig. (3-2) shows the variation of emission intensities with laser irradiance, distance along

the plume and ambient pressure. The emission intensities of four silicon lines produced by 1064

nm at 2–12 GWcm−2

laser irradiance is shown in Fig. (3-2a). This figure illustrates that initially

at low laser irradiance, the signal intensity increases almost linearly but at higher irradiance (5–

12 GWcm−2

) the increasing rate is relatively slow. Beyond 12 GWcm−2

, the intensity variation

becomes small as clear from the 288.16 nm transition but saturation is not observed. However, in

all previously reported work, saturation effects in the 288.16 nm line are observed at higher laser


37

irradiance. For example, Liu et al. [100] observed an increasing trend in the intensity of the

288.16 nm line up to 23.7 GWcm−2

and saturation appeared around 29 GWcm−2

. Milan and

Laserna [31] reported the emission intensity of the 288.16 nm silicon line from 0.2 to 45

GWcm−2

, which shows an increasing trend up to 20 GWcm−2

and thereafter a clear saturation is

observed from 20 up to 45 GWcm−2

.

The spatial distribution of silicon emission lines up to 5.0 mm at 10 GWcm−2

is shown in

Fig. (3-2b). In this figure, the intensities are maximum in the central region of the plasma (∼2–3

mm from the target surface) and show a decreasing trend toward the edges, which indicates that

the core of the plasma is hotter than the exterior of the plasma. The spatial behavior observed in

this work is in agreement with that of Liu et al. [100] having maximum intensity at 1.8 mm.

However, Milan and Laserna [31] reported the maximum intensity around 0.2 mm for neutral

and ionic transitions. Fig. (3-2c) shows the ambient pressure dependence on the emission line

intensities of silicon lines at low pressures from 45 to 550 mbar at 5 GWcm−2

.

(a)

3P

13

s 3p

3 3D

2 →

3s2

3p

2 3

P1

3s2

3p

4s 3

P0 →

3s2

3p

2 3P

1

3s2

3p

4s 1

P1 →

3s2

3p

2 1D

2

3s2

3p

3d

1P

1 →

3s2

3p

2 1S

0


38

240 250 260 270 280 290

0

500

1000

1500

2000

2500

3000

5.55

4.54

3.53

2.52

1.51

3s2

3p 4

s 3

P0

3

s2 3

p2 3

P1

3s2

3p 3

d 1P

1

3s2

3p

2 1S

0

3s2

3p 4

s 1P

1

3s2

3p

2 1

D2

Sig

nal

In

ten

sity

(a.

u)

Dista

nce (m

m)

Wavelength (nm)

240 250 260 270 280 290

150

200

250

300

350

400

450

500

550

600

360

170

56

29

14

3s2

3p 4

s 3P

0

3s2

3p

2 3

P1

3s2

3p 4

s 1P

1

3s2

3p

2 1

D2

3s2

3p 3

d 1P

1

3s2

3p

2 1S

0

Press

ure (m

bar)

Wavelength (nm)

Inte

nsi

ty (

a.u)

Figure 3-2: Variation of emission intensities of the selected silicon lines, acquired through

1064 nm laser ablation, with (a) laser irradiance, (b) distance from the target surface and

(c) with ambient pressure.

(c)

(b)


39

At low pressure, the lack of external ambient confinement causes weak emission

intensity, whereas at high pressures collisions with the ambient gas result in intense emission

lines. Amal et al. [104] reported an increase in LIBS signal intensity up to 500 mbar, which is in

agreement with this work.

3.3.2 Laser Irradiance Dependence of Plasma Parameters

The recorded emission spectra have been used to estimate the electron temperature and the

electron number density. To determine the temperature, the Boltzmann plot method has been

used assuming that plasma is in local thermodynamic equilibrium and is optically thin. The

emission lines used in these plots were free from spectral interference, unsaturated and their

spectroscopic data are listed in Table 3-1. The exemplarily Boltzmann plots of Si emission lines,

recorded at 11.4 GWcm-2

as shown in Fig. (3-3). The Boltzmann plot yields the electron

temperature as 7000 ± 500 K. It is worth mentioning that the silicon emission spectra contain

only a few ionic lines, therefore only neutral lines are used for the determination of the electron

temperature. The uncertainty in the temperature determination is ~10%, which is due to the

uncertainty in transition probability, integrated intensity, and in fitting procedure.

Table 3-1: Spectroscopic data of silicon emission lines used for determination of electron

temperature.

Wavelength (nm) Transitions Statistical weight

of upper state gm

Transition

probability

A ( 107s

-1)

Upper Energy

Level (cm-1

)

212.29 3s2 3p3d

1P1→ 3s

23p

2 1D2 3 3.57 53387.33

221.09 3s2 3p

3 3D2→ 3s

2 3p

2 3P1 5 3.46 45293.63

243.51 3s2 3p3d

1D2 → 3s

23p

2 1D2 5 4.43 47351.55

252.41 3s2 3p4s

3P0 → 3s

2 3p

2 3P1 1 22.2 39683.16

252.85 3s2 3p4s

3P1 → 3s

23p

2 3P2 3 9.04 39760.28

288.16 3s2 3p4s

1P1→ 3s

2 3p

2 1D2 3 21.7 40991.88


40

Figure 3-3: Boltzmann plot for the determination of electron temperature using neutral

silicon emission lines yield the electron temperature as 7000 ± 500 K at 11.4 GWcm-2

irradiance of 1064 nm laser wavelength.

The laser irradiance dependence of silicon plasma is given in Fig. (3-4), showing the power law

fitted trend in temperature with respect to laser irradiance (2 to 16 GWcm−2

) from 6350 to 7000

K and 6000 to 6400 K corresponding to laser ablation at 1064 and 532 nm. The high electron

temperature for 1064 nm in comparison with 532 nm is because of the efficient laser absorption

due to higher value of inverse bremsstrahlung (IB). The electron temperature raises up to 5

GWcm−2

and thereafter saturation effect starts appearing due to plasma shielding. The electron

temperature reported by Milan and Laserna [31] at 10.6 GWcm−2

of 532 nm is in good

agreement with this work. However, a similar increasing trend in electron temperature at 2–80

GWcm−2

laser irradiance of 266 nm is reported by Liu et al [100], revealing much higher

electron temperatures (1.5–80) ×104 K.

The electron number density is another important plasma parameter which provides the behavior

of plasma under different experimental conditions and ambient environment. The electron

number density of laser induced plasma can be determined using the Stark broadening in the line


41

Figure 3-4: Variation of electron temperature of Si plasma, as a function of laser irradiance

from 2 to 16 GWcm-2

of 1064 nm and 532 nm of Nd: YAG laser.

profile [37, 106]. The line broadening is mainly due to the Stark effect, whereas other sources of

broadening such as Doppler and resonance broadening are negligible. However, the instrumental

broadening cannot be ignored; therefore, the line profile was corrected by subtracting the

contribution of the instrumental broadening (0.04 nm).

The FWHM of the silicon emission line 3s2

3p3d 1

P1 → 3s2

3p2 1

D2 at 212.29 nm is used

in Eq. (1-22) and the electron number density of the order of 1016

cm−3

has been extracted. The

uncertainty in the determination of electron number density is ∼15%, which is mainly due to the

uncertainties in the electron impact parameter, FWHM and in the deconvolution of the line width

to the instrumental width. The electron number density as a function of laser irradiance 3–16

GWcm−2

is plotted in Fig. (3-5), which show an increasing trend from 3.42 × 1016

to 4.44 × 1016

cm−3

and 4.20 × 1016

to 5.72 × 1016

cm−3

for 1064 nm and 532 nm, respectively. The solid lines

are the power law fitting, indicating the increasing trend with laser irradiance. It is observed that

for 532 nm laser ablation the number density increases at a faster rate throughout the irradiance

range; however, for 1064 nm, a slow increase at low irradiance and saturation effects at higher


42

Figure 3-5: Variation in the electron number density of Si plasma as a function of laser

irradiance.

laser irradiance is observed. Liu et al. [100] reported much higher electron number density and

linear increase up to 55 GWcm−2

.

Milan and Laserna [31] used relatively low irradiance 0.2–45 GWcm−2

but their reported

number density is still higher as compared to the present work. It is observed that the number

density is high for 532 nm than for 1064 nm wavelength, which is attributed to the high ablation

rate for 532 nm [107] due to strong laser–matter coupling. Furthermore, laser–matter interaction

depends on the reflectivity of the target material, which is high for 1064 nm than 532 nm;

therefore, more mass ablation is observed for 532 nm. In addition to the reflection from the

sample surface, the laser beam is also reflected or absorbed from the plasma, depending on the

plasma frequency vp [108]:

5.03109.8 ep Nv

(3-1)

According to this equation, the frequency of plasma at maximum electron number density

(5.72 × 1016

cm−3

) is ≈ 2.13 × 1012

Hz, whereas for 1064 nm and 532 nm the laser frequencies

are 2.8 × 1014

Hz and 5.6 × 1014

Hz, respectively. As the frequency of laser light is more than the


43

plasma frequency, therefore, laser energy gets absorbed in the plasma, which results efficient

ablation.

3.3.3 Spatial Dependence of Plasma Parameters

Fig. (3-6) shows the spatial variation of electron temperature of silicon plasma along the plume

length up to 5.0 mm at a fixed laser irradiance of 10 GWcm−2

. The solid lines show the power

law fitting over the experimental data points. At 1064 nm, the electron temperature decreases

from 8200 to 6300 K and for 532 nm it varies from 6400 to 5500 K. The electron temperature

close to the target is high, and decreases with increasing distance up to 5.0 mm from the target

surface. The higher temperature near the sample is because of higher plasma expansion and

cooling rates, whereas at 2.5 mm from the target surface, recombination control the plasma

decay [109], which results a decrease in the electron temperature. This type of trend is reported

by many people [106, 109-111].

Figure 3-6: Spatial distribution of the electron temperature of Si plasma.


44

Figure 3-7: Spatial distribution of the electron number density Si plasma.

Similarly, the spatial distribution of the electron number density as shown in Fig. (3-7),

has maximum value close to the target surface, which decreases up to 5.0 mm. The solid line

passing through the data points is the power law fit, indicating the decreasing trend in electron

number density with increasing distance. Close to the target surface, more energy is absorbed

leading to efficient ionization [112], whereas at later stage recombination starts, which

compensates the ionization rate and decreases the electron number density.

3.3.4 Pressure Dependence of Plasma Parameters

The ambient environment strongly affects the size, shape, propagation speed, and the emission

properties of the laser induced plasma [113]. In order to study the effects of ambient pressure on

laser induced silicon plasma, the electron temperature and electron number density have been

determined at different ambient pressure. The ambient pressure dependence of silicon plasma

temperature from 45 to 550 mbar is shown in Fig. (3-8), which shows an increase in electron

temperature from 4850 to 5440 K up to 250 mbar and thereafter no variation up to 550 mbar was

observed. The increasing trend up to 250 mbar is due to the increase in plasma confinement,


45

Figure 3-8: Variation of electron temperature of Si plasma with ambient pressure from 45

to 550 mbar at fixed irradiance of 1064 and 532 nm of Nd: YAG laser.

increased rate of recombination, collisional excitation and short mean free time and mean free

path. The pressure dependence studies of Cowpe et al. [105] reported elevated temperatures at 10

and 100 mbar than 1000 mbar. Amal et al. [104] observed that the temperature with inter-pulse

delay and pressure change reveal a significant variation of 7000–11600 K at 0.7, 470 and 1000

hPa. Fig. (3-9) shows that as the pressure increases from 45 to 550 mbar, the electron number

density increases from 1.51 × 1016

cm−3

to 2.12 × 1016

cm−3

and 1.7×1016

cm−3

to 2.45×1016

cm−3

for 1064 nm and 532 nm, respectively. The solid lines are the power law fit over the electron

number density, indicating the overall trend with pressure. The electron number density increases

at a faster rate up to 200 mbar, whereas at increased pressure the plasma shielding limits the

increasing rate and saturation starts at around 300 mbar. The pressure dependence of the electron

number density in silicon plasmas is reported by Amal et al. [104]. Their measurements at

atmospheric pressure 0.7, 470 and 1000 hPa show much faster increase than the present

measurements. Subsequently, Cowpe et al. [105] reported an increasing trend for electron

number density in the range 2.79 × 1017–5.59 × 10

19 cm

−3 at pressure of 10

−4 to 10

3 mbar.


46

Figure 3-9: Variation of electron number density of Si plasma with ambient pressure from

45 to 550 mbar at fixed irradiance of 1064 and 532 nm of Nd: YAG laser.

The increasing trend in electron temperature and number density with ambient pressure is

due to the confinement of plasma in a small region leading to enhanced rate of collisional

excitation and recombination. Finally, the condition for LTE and plasma opacity was verified for

Si plasma. The necessary condition for the existence of LTE is verified using the following

relation [114]:

332/114104.1 cmETN ee

(3-2)

Here T (K) is the electron temperature and E (eV) is the energy difference between the

upper and lower levels. Using electron temperature (7200 K) and the energy difference of the 3s2

3p3d 1P1→ 3s

2 3p

2 1D2 silicon transition (5.83 eV), the number density of electrons is calculated

as 2.70×1016

cm−3

, which is greater than the limit defined in Eq. (3-2); therefore, the criterion of

LTE is verified. However, this criterion is a necessary but not the only requirement for LTE. The

opacity of silicon plasmas is verified using the Si I (288.16 nm) line, which is the most

prominent line in all emission spectra. This line is recorded at different laser irradiances and no


47

saturation effects are observed even at maximum irradiance, which confirms that the plasma

recorded in this work, is optically thin.

Germanium is also a very important semi-conductor material having various applications

as an alloying agent to enhance the refractive index of glasses and as a substrate wafers for

efficient solar cells production [115]. The laser induced germanium plasma has been produced

using 1064 of Nd: YAG laser and the emission spectra have been characterized as function of

various experimental parameters such as laser irradiance, distance from the target surface and

ambient pressure.

As the core work in the thesis is on the calibration free LIBS (CF-LIBS) analysis of

various alloys which contains silicon and germanium as major constituents. The CF-LIBS

technique requires emission line intensity and plasma parameters (plasma temperature and

electron number density) for the quantitative analysis of all species present in a sample.

Therefore, the understanding, determination and the dynamics of plasma parameters with laser

irradiance, ambient pressure and distance from the target surface are useful for CF-LIBS

analysis.

48

Chapter 4

Calibration Free Laser Induced Breakdown 4

Spectroscopy of Al-Si Alloy

4.1 Introduction

Laser induced breakdown spectroscopy (LIBS) is a well-established atomic spectroscopy

based analytical approach of all kind of samples. LIBS is considered an effective approach for

reliable multi- elemental analysis in closed contact and standoff arrangement. The quantitative

analysis is carried out either through calibration curves, constructed using standard reference

material or plasma parameters and line integrated intensities. To build calibration curves, the

matrix matching of the target and reference samples is mandatory. However, there may be

situations when matrix matching does not exist between reference samples and the sample under

study [116]. To overcome the matrix matching issue, different approaches were adopted [117-

120]. As an alternative of using reference samples and calibration curves, Ciccu et al. [121]

introduced the calibration free LIBS (CF-LIBS) technique, in which line intensity and plasma

parameters are used for the quantitative analysis of all species present in a sample. In subsequent

years, this was used for the quantitative analysis of precious alloys [122], metallic alloys [123-

126], non-metallic alloys, and soil samples [116, 124, 127]. Tognoni et al. [128]

comprehensively reviewed the basic idea of calibration free LIBS and its application in various

fields and suggested that CF-LIBS is more accurate in analyzing metallic alloys than dielectrics.

CF-LIBS has some limitations and approximations such as stoichiometric ablation, validity of

locally in thermodynamic equilibrium (LTE), plasma thickness, and plasma spatial homogeneity,

which have also been discussed in this review. In order to improve the accuracy, many variants

of this technique are reported in literature [129, 130], including the use of numerical procedure

[125, 131], double pulse LIBS [132], and eliminating self-absorption in the spectra, leading to

Chapter 4: Calibration Free Laser Induced Breakdown…

49

more accurate plasma temperature [133]. Unnikrishan et al. [134] used appropriate time delay

where the LTE condition is fulfilled, resulting more accurate plasma parameters and hence

accurate quantitative analysis. These efforts made the CF-LIBS approach a sufficiently reliable

quantitative analysis technique; however, more attention is needed to make it reliable than

existing analytical techniques.

The CF-LIBS technique utilizes plasma temperature and line emission intensities for the

compositional analysis of samples. The plasma parameters, particularly the temperature, provide

better understanding of the laser matter interaction and can be used for the compositional

analysis. To get accurate plasma temperature, background subtraction and self-absorption

correction in emission lines have important role. Therefore, in order to remove the self-

absorption in emission line intensities, different approaches were used, as described in first

chapter. In addition to self-absorption correction, some other experimental factors such as laser

energy, acquisition delay, and background subtraction need to be optimized for reliable

quantitative analysis. In the present work, we have used the standard Al-Si alloy for the

quantitative analysis of all the major and trace elements in a sample. The trace impurities in

silicon based alloys are important because several impurities like Fe, Cr, Ni, and Cu even at ppm

level can significantly affect the solar cell performance [135]. In 2011, Sabatino et al. [136]

determined the impurities in the metallurgical grade silicon (Mg-Si) alloy using glow discharge

mass spectrometry (GDMS). Hornackova et al. [137] determined the Si to Al molar ratio in

microporous zeolites using calibration free LIBS laser induced breakdown spectroscopy (CF-

LIBS).

The objective of the present work was to make the calibration free LIBS a more accurate

and reliable quantitative analysis technique. For this purpose, the plasma was produced at

different laser irradiance values; distance along plume length, at different delay times and the

optimized experimental conditions were deduced. Furthermore, the emission intensities of the

sample constituents were background subtracted and corrected for self-absorption. The

improvement in accuracy of CF-LIBS results due to these optimization and corrections was

investigated. The results of quantitative analysis before and after self-absorption correction were

reported with 0.3–2.2% deviation from the reference data.


50

4.2 Experimental Details

The schematic diagram of the experimental setup is presented in Fig. (2-8), which

consists of Nd: YAG laser, operating at 1064 nm wavelength of 30–200 mJ pulse energy, 9 ns

pulse duration, and a repetition rate of 10Hz. The sample was irradiated with laser beam, focused

with a lens of 10 cm focal length that yields a spot size of approx. 300 µm and laser spot area of

7.1 x10-4

cm2 at the focus. The Al-Si alloy in the form of disc having surface perpendicular to the

laser beam was fixed on a motorized X, Y, Z rotational stage to expose fresh sample position

each time. The alloy consists of Al, Si as a major constituent whereas all other elements are

present in trace quantity. The sample used in the present experiments was standard alloy

(Spectroscopic Standard No. S.S 505, Bureau of Analyzed Samples, England) with known

concentration. The sample was washed and the surface was cleaned by firing ten laser shots of

low energy. Thereafter, the focused laser beam was irradiated on the alloy to create plasma on

the sample surface. The rest of the experimental procedure is the same as described in

experimental detail’s chapter.


4.3.1 Optimization of the Experimental Parameters

The reliable quantification via calibration-free approach need to optimize the ablation

parameters such as laser irradiance, lens to sample distance, spectral response of the

spectrometer, detector gate width, and acquisition delay need to be optimized. The laser

irradiance was varied from 4.7 to 31.5 GWcm-2

and the corresponding emission spectra were

recorded. At low laser irradiance (7.9 GWcm-2

), only the emission lines of major constituents

and resonance transitions of trace elements in Al-Si alloy were detected, whereas at higher

irradiance the emission lines of major elements get saturated. It was also observed that the

continuum effects were pronounced at higher laser irradiance (>18.9 GWcm-2

). At an

intermediate irradiance (15.7 GWcm-2

), the trace elements were detected with a sufficient signal-

to- noise ratio (S/N) and the emission lines of major elements were sharp and free from

saturation. Therefore, in the present work, 15.7 GWcm-2

irradiance was used to produce plasma.

Initially, the plasma emissions have continuum and weak emission lines of trace elements are not

distinguishable. To reduce the continuum effects and to get better S/N ratio, the data acquisition


51

delay (gate) was varied from the 0 to 6 µs in steps of 0.5 µs. The corresponding emission spectra

were recorded and plotted versus gate delay, which yield maximum signal enhancement at 3.5 µs

gate delay. Similarly, the lens to sample distance (LTSD) was optimized for accurate and

reproducible results. Even keeping the laser energy fixed, a slight change in LTSD causes a

significant change in laser irradiance, which affects the emission intensities. This distance was

observed by taking a burn pattern at different LSD and was optimized at 10.2 cm. Furthermore,

the plasma emissions were captured with fiber moved up to 3 mm along the plume length. The

analysis of the recorded spectra yields maximum signal intensity of sample constituents Al, Zn,

and Ni lines at 1.8 mm. At this location, the plasma parameters were extracted, which satisfy

LTE conditions. The spectrometer’s spectral response was corrected by calibrating intensity

using the standard intensity calibrated lamp following the procedure provided for Ocean optics

spectrometers. The wavelength calibration was done using standard Hg-Ar lamp and coefficients

were updated from regression analysis. The above mentioned optimized parameters were used to

record the emission spectra of alloy for the quantification their contents.

4.3.2 Analysis of the Emission Spectra

Fig. (4-1) represents the portion of the alloy emission spectra, in the spectral range 220 to 290

nm, which consists of various strong and weak emission lines of the elements present in alloy.

Generally, the strong emission lines belong to major constituents, whereas the weak lines come

from trace species. Analysis of the emission spectra was performed using Matlab package based

on the linear correlation with NIST atomic database [93]. In order to avoid false assignment of

the emission lines, the relative intensity ratio of the lines was compared with the relative

intensity ratio reported in literature. Only those elements declared “detected” having many

spectral lines in the emission spectra. The complete spectra from 220 to 720 nm consist of more

than hundred spectral lines and their analysis confirmed the presence of eleven elements, Mg, Al,

Si, Ti, Mn, Fe, Ni, Cu, Zn, Sn, and Pb in the Al-Si alloy. Most of the emission lines lie in the UV

and visible region of the spectra whereas the Hα line at 656.28 nm and few weak lines of nitrogen

and oxygen are detected in the NIR region of the spectra. It is worth mentioned that the laser

beam was focused inside the sample surface that reduced air breakdown and therefore weak

emission lines of nitrogen and oxygen were detected.


52

Figure 4-1: Portion of the single pulse LIBS spectra of Al-Si alloy, acquired at a laser

irradiance of 15.7 GWcm-2

of 1064 nm of the Nd: YAG laser.

The emission lines of Al and Si are mostly observed in the 220–400 nm range, whereas

Mg, Ti, Mn, Fe, Ni, Cu, and Zn are detected in the 300–500 nm band of the spectra. The

emission spectra are rich in neutral emission lines but few singly ionized lines of Mg, Fe, Mn, Si,

and Ti were also detected. According to Herrera et al. [126], calibration free LIBS results are

more accurate when one species of an element is dominant in the emission spectra as compared

when their abundance is balanced. In LIBS spectra, the analyte signal may be camouflaged by

background emissions appeared either due to bremsstrahlung or electron–ion recombination

processes. These emissions may interfere with the line intensity and consequently reduce the

accuracy of results [138]. Fig. (4-2) shows the observed spectrum recorded at 3.5 µs gate delay

to reduce the background continuum effects. Furthermore, the background has been subtracted in

small spectral steps using the polynomial based Matlab code. The lower trace in this figure is the

background-subtracted spectrum, which improves the accuracy of CF-LIBS quantitative

analysis. This yields the intensity ratio of multiplets, which are in accordance with the intensity

selection rules.


53

Figure 4-2: The upper trace is the original spectra whereas the lower trace is the

background subtracted spectra of the Al-Si alloy.

In order to get accurate plasma parameters and quantitative analysis, the laser induced plasma

must be optically thin and in local thermodynamic equilibrium (LTE). The assumption of

validity of LTE can be confirmed by using McWhirter’s criterion [15]:

332/114104.1 cmETN ee

(4-1)

The measured electron number density is represented by Ne (cm-3

), the plasma

temperature by Te (eV) and ∆E (eV) is energy corresponding to transition with maximum energy

spacing. The electron number density was determined from the Stark broadened Hα line

according to Eq. (1-24). The use of Hα line for the determination of electron number density is

the most appropriate because Hα line is least self-absorbed due to its low concentration in the

ambient environment. The electron number density may be affected by Doppler broadening,

resonance, and Stark broadening. Among which, the Doppler and resonance broadening can

safely be ignored and only the Stark broadening is considered for the measurement of electron

number density. Since the plasma was generated with laser irradiance (4.7–31.5 GWcm-2

),

correspondingly, the electron number density was evaluated that shows an increasing trend with

laser irradiance. At 15.7 GWcm-2

, the electron number density 2.4x1017

cm3

is neither low nor

saturated; hence, it is used as an optimized parameter in the present work. This value of electron


54

number density is sufficiently higher compared when calculated at a temperature of 10100 K and

3.23 eV energy difference. Hence, the assumption of validity of LTE is fulfilled in the present

case.

4.3.3 Self-Absorption Correction in Emission Spectra

In CF-LIBS, the emission line intensities are used to determine the plasma temperature and

species concentration in a sample. Therefore, the true values of integrated intensities of the

selected emission lines are mandatory. The presence of self-absorption in a line profile reduces

line intensities from their actual values [139], leading to inaccurate quantitative analysis. Self-

absorption appears when plasma light re-absorbed by the cold atoms along the optical path

length making line profile flat top or in extreme cases a dip appears in the line center [140].

Various methods were developed to overcome this issue. Bulajic et al. [141] used the curve of

growth method (COG) for self-absorption correction. They utilized plasma parameters, optical

path length, Gaussian and Lorentzian broadenings for this purpose. Sherbini et al. [38] compared

the elemental line intensities with non-self-absorbed Hα line present in the same emission spectra.

Later, Sun and Yu [142] used the emission line of the same species having lower transition

probability and higher excitation energy as a reference line and extracted the self-absorption

coefficient from their ratio with the line of interest. Praher et al. [143] corrected the self-

absorption by using the iterative procedure incorporating optical depth, path length, number

density, and full width at half maxima (FWHM) of the optically thick line profile. In the present

work, we applied the internal reference method [133, 142] to evaluate and correct the self-

absorption in the selected emission lines. The details of this method are outlined in first chapter.

Table 4-1 lists the selected emission lines used for self-absorption evaluation and

subsequently for the determination of plasma temperature. The determination of self-absorption

(SA) coefficient requires the plasma temperature, which is extracted from the Boltzmann and

Saha Boltzmann plots built using uncorrected line intensities. The extracted self-absorption

coefficients (SA) are used in SAII Corr

to get new integrated intensities, which are used in

Boltzmann and Saha Boltzmann plots to get new temperature. This procedure of SA correction

and temperature determination is iterated until the correlation coefficients of linear fitting on

Boltzmann and Saha Boltzmann plots converged.


55

Table 4-1: List of the selected emission lines used for self-absorption evaluations and

Boltzmann plots. The wavelengths highlighted in bold are internal reference lines.

Species Wavelength (nm)

Mg I

Mg II

Al I

Si I

Si II

Ti I

Ti II

Mn I

Mn II

Fe I

Fe II

Ni I

Cu I

Zn I

Sn I

Pb I

383.23, 383.23, 382.94, 518.36

279.55, 279.80, 280.27, 266.07

257.51, 266.04, 396.15, 309.27

252.85, 252.41, 250.69, 251.92, 288.16, 243.51, 288.16

634.71, 637.14, 385.60, 413.09

428.88, 482.04, 484.09, 432.51

334.95, 336.12, 337.28, 338.37, 376.13, 334.94

403.08, 404.14, 405.55, 408.29

259.37, 260.57, 293.31

342.71, 346.59, 349.06, 427.11, 430.79, 344.06

503.57, 542.99, 645.64, 552.91

336.96, 338.06, 341.48, 343.35, 344.63

510.554, 521.82, 465.11,427.51

330.29, 481.05, 328.23, 334.50

283.99, 317.5, 326.23

261.41, 363.95, 373.99

The final temperature and integrated intensities are then used in CF-LIBS calculations.

The Boltzmann plot method is used for the determination of plasma temperature that utilizes line

intensities of the same species and same ionization stage. Whereas in the Saha Boltzmann plot

method the emission intensities from different ionization stages are used to extract temperature,

which results more accurate plasma temperature and consequently reliable compositional

analysis of the target sample [32].

Fig. (4-3) shows the Saha Boltzmann plots of Ti-lines with and without self-absorption

correction in emission intensities. The raw data points on the Saha Boltzmann plot (solid

squares) are scattered resulting linear correlation with 0.97 adjusted R2

value. However, after

self-absorption correction (solid circles), the data points become smooth with good linear

correlation (adjusted R2

0.99). The solid red lines are the linear fitting over the uncorrected and

corrected data points, which yield the plasma temperature as 10400 and 10100 K, respectively.

The uncertainty in plasma temperature after self-absorption correction is 3%, which is mostly

due to uncertainties in transition probabilities, integrated intensities, and fitting procedure. It is

worth mentioned that the correction in self-absorption modified the plasma temperature by 300

K, which is comparable to the associated uncertainty in temperature.


56

Figure 4-3: Saha Boltzmann plot using Ti lines with and without self-absorption correction

in integrated intensities.

This correction in the value of temperature may be attributed to the self-absorption correction,

optimized experimental parameters and background subtraction from the emission spectra.

4.3.4 Quantitative Analysis of Al-Si Alloy

The procedure of quantitative analysis using calibration free LIBS is described in detail in second

chapter. This technique is based on the idea that integrated intensity of the emission line is

proportional to the species concentration with the assumption that the plasma is optically thin and

in local thermodynamic equilibrium (LTE). This technique utilizes the plasma temperature,

which was extracted from Boltzmann plot of neutral lines. Since the emission spectra of the Al-

Si alloy also contain singly ionized lines of Mg, Si, Ti, Mn, and Fe, in order to include their

contribution in elemental concentration, the Saha Boltzmann plots (See Eq 1-18) have been built

using integrated intensities of singly ionized lines. Other parameters required for calibration free

analysis, are the experimental factor F, intercepts for each species, and the partition functions for

all species. These parameters are used in Eq. (4-2) to get the elemental concentration of the Al-Si

alloy.


57

F

eTUeTUC

IIS

IS q

e

II

S

q

e

I

SS

(4-2)

To perform compositional analysis of the Al-Si alloy, we select the emission lines of each

species that are free from spectral interference, non-resonance, and having large difference in

their excitation energies. These lines were corrected for self-absorption and used in Boltzmann

plots.

Fig. (4-4) and (4-5) show the Boltzmann plots built using neutral emission lines before

and after self-absorption correction. It is evident from Fig. (4-4) that the data points of Cu, Zn,

and Pb are relatively more scattered due to self-absorption, and consequently, the slope and

intercept from linear fitting did not yield true values of plasma temperature and species

concentration. The data points of the remaining elements are less scattered and show linear

fitting with good correlation, which may be due to less self-absorption in the emission lines.

Figure 4-4: Boltzmann plots of the species in the alloy without self-absorption correction.


58

Figure 4-5: Boltzmann plots of the species in the alloy with self-absorption correction.

After correcting emission intensities, the Boltzmann plots have been rebuilt in Fig. (4-5),

which show good correlation and the data points, are stretched along the fitted lines. Thus, the

extracted plasma temperature and intercepts are relatively more accurate.

The Boltzmann plots are built using singly ionized lines of Mg, Si, Ti, Mn, and Fe as

shown in Fig. (4-6) and (4-7). These plots are built using integrated intensities before and after

self-absorption correction, illustrating good linear fit and consequently accurate plasma

temperature and intercepts are extracted. These parameters are used in Eq. (4-2) to determine the

elemental concentration of alloy.


59

Figure 4-6: Boltzmann plots of the ionized species in alloy without self-absorption

correction.

Figure 4-7: Boltzmann plots of the ionized species in alloy with self-absorption correction.


60

Figure 4-8: Elemental concentration of all the elements in alloy, except Al and Si.

Fig. (4-8) represents the concentration of all the elements except Al and Si due to clear

illustration of the trace elements. This figure shows that among trace elements, Mn and Fe have

more concentration, whereas Ti has the least concentration. The relative standard deviation

(%RSD) lies between 0.08% and 2%, which is less than that reported in literature 0.3 to 38%,

60.5 to 68%, and 0.05 to 21% [121, 133, 142].

Table 4-2 lists the results of the present work, their comparison with reference

concentration, and the percentage deviation from the reference data. In the case of uncorrected

data, the results are more deviated (0.6–6.7%) from the reference values, but very small

deviation (0.0–2.2%) is observed after self-absorption correction. These results clearly show that

SA corrections are very important in the emission spectra for more accurate quantitative analysis.


61

Table 4-2: Compositional analysis of Al-Si alloy with and without self-absorption

correction in the emission intensities.

Element

Elemental Concentration % age deviation from

reference data

Without self-

absorption

correction

With self-

absorption

correction

Reference data

Without

SA

With

SA

Mg

Al

Si

Ti

Mn

Fe

Ni

Cu

Zn

Sn

Pb

0.041

85.12

13.21

0.032

0.47

0.35

0.20

0.048

0.24

0.18

0.11

0.04

85.89

12.45

0.031

0.49

0.34

0.196

0.051

0.237

0.175

0.10

0.04

85.6

12.5

0.03

0.5

0.33

0.19

0.05

0.23

0.17

0.1

2.5

0.6

5.7

5.7

5.9

7

4.6

3.9

4

5.8

5.6

0.0

0.3

0.4

2.2

2.3

2.8

3

1.3

2.9

2.7

2.4

5

62

Chapter 5

Double Pulse Calibration-Free LIBS: Quantitative 5

Analysis of Ge/Si Alloys and Solar Cells

5.1 Introduction

The quantitative elemental analysis of industrial metallic and non-metallic alloys is routinely

carried out using analytical techniques such as Inductively Coupled Plasma Optical Emission

Spectroscopy (ICP-OES), Inductively Coupled Plasma Mass Spectroscopy (ICP-MS), Spark

Optical Emission Spectroscopy (Spark-OES), X-Ray Fluorescence (XRF) and Atomic

Absorption Spectroscopy (AAS) [144]. The above mentioned techniques are time taking, need

sample preparation, risk of sample contamination and analysis of light elements is often difficult.

Furthermore, these techniques are usually implemented in the laboratory; therefore, real time

analysis is not possible. However, Laser-Induced Breakdown Spectroscopy (LIBS) requires no

or very little sample preparation and experiments can be performed in situ [145]. In the first

chapter, the LIBS-based quantitative analysis techniques and its variants have been described in

detail. The calibration free technique is applied to analyze the precious alloys [122], to dielectric

and conducting materials [146] and bronze, brass, gold alloys, glass and archaeological samples

[124]. Most of the cited work used single pulse laser for the acquisition of emission spectra.

However, single pulse LIBS suffers from relatively low sensitivity and accuracy as compared to

the existing analytical techniques [104]. Therefore, dual pulse is used to improve the sensitivity,

selectivity and accuracy of the CF-LIBS results. Applied Laser Spectroscopy Laboratory in Pisa

developed a Mobile Dual-pulse LIBS instrument (MODI) [88], which has been used for the CF-

LIBS analysis of soil sample, synthetic emeralds grown by Biron hydrothermal method and for

the analysis of industrial waste molding and core sands [132, 147, 148]. To best of our

Chapter 5: Double Pulse Calibration Free LIBS: Quantitative…

63

knowledge, only few groups used double pulse calibration-free LIBS for the analysis of alloys.

Contreras et al. [149] used the Calibration-Free technique with orthogonal double pulse LIBS at

low ablative energies (0.25 & 7 mJ) for quantitative analysis of steel samples. Duan et al. [150]

performed a Calibration-Free quantitative analysis of copper alloy, using two pulses by splitting

single laser pulse with 1:1 ratio. The results agreed with certified compositions with accuracy of

± 15%.

The research presented here is the extension of our previous work performed on the

analysis of Al-Si alloy with single pulse calibration free LIBS, as discussed in the previous

chapter. The aim of the present work is to exploit and further improve the analytical capabilities

of DP-CF-LIBS by performing elemental analysis of Ge-Cu/Si and Ge-Ba/Si alloys. Germanium

and silicon are the major constituents of these alloys. Germanium was discovered at the end of

nineteenth century, although most of its industrial applications are much more recent, being

related to the production of optical fibers and semiconductors. Germanium and silicon have

similar chemical properties; therefore, they can substitute each other in a crystal lattice site with

perfect miscibility at all the concentrations [151]. Varying the stoichiometric ratio between Ge

and Si, the energy band gap between the valence and conduction band can be finely adjusted

[152]; therefore, the knowledge of this ratio is particularly important for industrial quality control

and for fundamental studies.

From the above work, we learnt that calibration free LIBS technique suffers from a

drawback, for example, the neutral emission lines of trace elements and lines of singly ionized

species are not enough to draw Boltzmann plots and get intercept for CF-LIBS analysis. Even if

sufficient emission lines are present in the spectra, it is time taking to select suitable emission

lines and draw Boltzmann plots. To overcome these drawbacks and to speed up the analysis

procedure, Pace et al. [147] determined the species concentration in waste foundry sands using

intercepts extracted from the Boltzmann plots. But the species of which one or two emission

lines were detected; their intercepts were extracted from the expression of line intensity and

subsequently determined the concentration of elements present in a sample. Later on, Fu et al.

[153] extracted the relative concentration of neutral species from line intensity rather than from

the intercept of Boltzmann plot, whereas the relative concentration of ionized species was

extracted from the Saha equation, which utilizes the concentration of neutral species and the

electron number density. The Saha Boltzmann plot was only used for the determination of


64

Plasma temperature. Recently, the same group published the comparative study of standard

reference line method (SRL), combination of one point calibration free LIBS (OPC) with SRL

and intercept method with OPC approach. To reduce the sources of error and to speed up the

analysis procedure, a series of experiments were performed on Gd/Ge/Si alloy using double

pulse in collinear configuration. The plasma temperature is extracted from Saha Boltzmann plot

and the intercepts corresponding to neutral species were calculated using line intensity

expression. To circumvent the error associated with determination of electron number density,

we used the intercepts for ionized species directly from the line intensity expression rather than

the Saha equation. This brings accuracy in results as well as speeds up the calibration free

procedure with a step towards online analysis in real environment. To compare the results, the

elemental concentration has been determined using intercepts and electron number density

obtained from Saha equation. Moreover, the calibration free quantitative analysis technique has

been extended to the analysis of solar cells with the aim to measure the concentration of trace

elements B, Al, Ti and Fe required in PV-Si [154]. This may be the route to online monitoring of

Upgraded Metallurgical Silicon (UMG-Si) refining process. In order to maintain the quality of

thin film solar cell, together with morphological and electrical characteristics, the chemical

composition of the products have to be monitored [155]. The impurities in solar cell are both

metallic and non-metallic and usually appeared when the polycrystalline ingot is used directly or

used to grow the single crystals [156].

5.2 Experimental Setup

The diagram of double-pulse experimental arrangement is presented in Fig. (2-9), consisting of

two Nd:YAG lasers operating at 1064 nm with total laser energy of both laser was set at 40 mJ.

The laser pulses were directed and focused on the sample surface with plano-convex lens of 5 cm

focal length, resulting spot size of 300-350 µm in diameter. These pulses were used in collinear

configuration, which produce and re-heat the plasma. The plasma emissions were received with

optical fiber and transmitted to LIBS 2500+ (Ocean Optics, USA) spectrometer. The samples

used in this study were Ge/Cu/Si, Ge/Ba/Si, Gd/Ge/Si alloys and solar cells. The alloys were

pelletized of approx. 1 to 1.5 cm in diameter and 0.3 to 0.5 cm thick and the solar cell pieces

were used in the dimension of 10x10 mm. The silicon solar cells from three different

manufactures were used and care was taken to avoid any contamination. The emission spectra


65

were recorded with 2.1 ms fixed gate width and 0.8 µs gate delay and twenty single shot spectra

were averaged to obtain the experimental data. The emission spectra were corrected by

subtracting dark spectra, which was recorded independently. In order to get the laser energies,

free from fluctuations, a small portion of laser beam was incident on the energy meter and only

those data sets were used having minimum energy variation.


5.3.1 Effect of Inter-Pulse Delay and Energy Ratio on the Emission Spectra

The analytical capability of double pulse LIBS could be improved by optimizing inter-pulse

delay and energy ratio between laser pulses. Fig. (5-1) shows the variation of line emission

intensities at different inter-pulse delays and energy ratio in collinear double pulse arrangement.

The intensities of spectral lines of neutral atoms of Ge at 265.12 nm, Cu at 327.39 nm and Cu at

529.25 nm show maximum signal enhancement at about 1.6 µs inter-pulse delay; thereafter, a

decreasing trend was observed up to 10 µs as shown in Fig. (5-1a). Similarly, the energy ratio of

the laser pulses was plotted by trying 1:1, 1:3, 3:5 and 1:7 ratios, while keeping the total energy

fixed at 40 mJ and inter-pulse delay at 1.6 µs. The results found in Fig. (5-1b) show maximum

signal enhancement at 1:3 energy ratios between the first and second laser pulses. Benedetti et al.

[157] used an Al-target to study the effect of laser pulse energy on the emission intensities of

double-pulse LIBS from 1:6 to 1:1 energy ratio and observed maximum signal enhancement at

an energy ratio of 1:3, which is consistent to our work. Using the optimized values of these

parameters, about three to five times signal enhancement has been achieved as compared to the

single pulse spectra recorded at 40 mJ laser energy.

Similarly, the inter pulse delay and energy ratio optimization in case of Gd/Ge/Si alloy

and solar cells have been evaluated. The optimum signal to noise ratio was achieved at 1.7 µs for

alloy and 0.83 µs for the solar cells. At these inter pulse delays; the optimized energy ratio was

1:5 for alloy and 1:3 for rest of the samples. The emission spectra recorded under these

optimized conditions show five times signal enhancement than single pulse spectra, produced at

same total energy.


66

Figure 5-1: Emission intensities as a function of (a) inter-pulse delay and (b) laser

energy ratio. The vertical lines indicate optimized values of inter-pulse delay at 1.6

μs and 1:3 energy ratios, respectively.


67

5.3.2 Analysis of LIBS Spectra

The stoichiometric ablation is one of the key requirements in CF-LIBS analysis. Since, the

plasma generation using conventional single pulse suffers from low sensitivity and poor limit of

detection, therefore, there is a chance that trace constituents don’t appear in the corresponding

emission spectra and lost the stoichiometric ablation. To address this issue, double pulse LIBS

has been used, which results more focal volume, enhanced emissions, and consequently, the

trace species can be detected with good signal-to-noise ratio. Fig.(5-2) shows the double pulse

spectra recorded at 10+30 mJ laser pulse energies, superimposed on the emission spectra of

single pulse captured with same total energy. The comparison shows that double pulse spectra

are more intense and more emission lines (represented by arrows in the figure) are detected as

compared to single pulse spectra. The multiplet of silicon emission lines around 251 nm is not

detected in the single pulse spectra, but appeared with good signal to noise ratio in double pulse

LIBS spectra. In double pulse spectra, it was observed that the air constituents (oxygen and

nitrogen) were not enhanced in comparison to single pulse spectra. Cristoforetti et al. [158]

suggested that it is due to the generation of shock waves due first laser pulse, which creates a

low-pressure medium for the second laser pulse. The double pulse emission spectra of Ge-Cu/Si

and Ge-Ba/Si alloys were analyzed using Matlab package and NIST atomic database [93]. The

intensity selection rules have been used during the analysis, which not only improved the

accuracy of analysis, but also enabled estimation of the plasma optical thickness.

The complete spectra from 220 to 800 nm consist of more than hundred emission lines of

Ge, Cu, Si and Ge, Ba, Si in both alloys. The spectral range covering UV and visible, contains

the emission lines these elements, whereas the H, O and N emission lines are observed in the

NIR region. The presence of H emission line in Ge/Cu/Si plasma is due to the moisture in the

ambient air. However, dual pulse LIBS, Senesi et al. [159] experimentally demonstrated that the

hydrogen signal from metallic alloys is the same as the signal from the sample’s element. A

different behavior is observed for the signal from atmospheric oxygen and nitrogen, which

mainly comes from the plasma periphery.


68

Figure 5-2: Portion of the double and single pulse emission spectra, recorded at 40 mJ total

laser energy. The arrows represent the emission lines detected only in double pulse spectra.

A portion of the Gd-Ge/Si alloy spectrum is shown in Fig. (5-3), containing single and

double pulse spectra for comparison. It is evident from the figure that the emission lines in the

230-250 and 290-300 nm regions are hardly detected and cannot be used for qualitative or

quantitative analysis. We also observed many times signal enhancement in solar cell samples and

the detection of trace elements become possible.

The qualitative analysis of the emission spectra have been performed using Matlab

package and NIST atomic database [93]. In addition, the emission line intensities have been

checked to follow intensity section rules. The analysis of the spectra revealed multiple emission

lines of Gd, Ge and Si. It is worth mention that singly ionized emission lines of Gd and Ge were

detected but any ionized line for Si was not identified, may be due to less concentration in alloy.

In solar cell #1, the emission lines of Si, Al, C, Ti, Pb, Ca, K, Cu, Li, Na and Ag were detected.

Except Si, rest of the elements was discovered with weak emission intensities, indicating their

low level of concentration.


69

Figure 5-3: The upper trace is the emission spectra recorded with collinear double pulse

arrangement at 10 +30 mJ laser energies, whereas the lower spectra is single pulse spectra

with same total energy of 40 mJ.

In Solar cell #2 and #3, Si, Al, C, Li, Ag, Pb, Ti, Ca, K, C, Ti, Na) and Si, Al, Pb, Ca, Cr,

Li, K, In, Fe, Sn, Sb, Na, Ti, Cu, Na, Sr and Ba have been detected respectively. In the emission

spectra of solar cell samples, many strong lines of Si were observed which show their higher

concentration in the solar cells, whereas, other elements with few weak emission lines indicating

their low concentration. Only those emission lines have been selected which were free from

spectral interference, non-self-absorbed and the necessary spectroscopic data are available in

literature [93, 160]. These emission lines were then used for the estimation of plasma

temperature, electron number density and for the compositional analysis using CF-LIBS.

5.3.3 Plasma Temperature and Electron Number Density

The plasma temperature and electron density are the main parameters for compositional analysis

using calibration free LIBS. Due to the transient nature of the laser-induced plasma, these

parameters vary within the plasma lifetime and therefore their determination with time-integrated


70

Instrument, such as the LIBS 2500+ (used in this work), seem an impossible task. However,

Grifoni et al. [161] demonstrated that, in typical LIBS conditions, the fast decay of the LIBS

signal introduces a sort of time resolution in the spectra acquired with time-integrated

spectrometers, which can be estimated equivalent to about 1 s gate in time-resolved systems.

Exploiting this finding, the plasma temperature was estimated from the Saha-Boltzmann plot,

which is an extension of the conventional Boltzmann plot Method [32]. Fig. (5-4) shows the

Saha-Boltzmann plot built from the neutral and singly ionized emission lines of copper in Ge-

Cu/Si alloy. The iterative based linear fitting procedure extracted plasma temperature as 11600 ±

300 K.

Similarly, the plasma temperature for Ge-Ba/Si alloy has been measured as 7700 ± 200

K. The intercepts of neutral and singly ionized species for the rest of elements obtained from

Boltzmann plots as illustrated in Fig. (5-5) was used in CF-LIBS calculations. It was observed

that these temperatures are same within the experimental uncertainty, which indicate that the

Figure 5-4: Saha-Boltzmann plot obtained from Cu I and Cu II emission lines

in collinear double pulse configuration with 1.6 µs inter-pulse delay and 10 +30

mJ laser pulse energies.


71

Figure 5-5: Boltzmann plots of neutral and ionized emission lines of the species present in

Ge-Cu/Si alloy. The solid lines are the linear fitting over the experimental data points.

plasma is in local thermodynamic equilibrium. As the existence of LTE is necessary for a

reliable Calibration-Free analysis, hence its validity was further investigated by considering two

more criteria. The first was the McWhirter criterion [15], which is necessary but not sufficient

condition for the plasma to be in LTE. In the present work, the McWhirter’s criterion was

satisfied, i.e. the collisions were dominant over the radiative phenomena. The second criterion is

the determination of relaxation time ( ) and plasma diffusion length ( [162]. According

to this criterion the relaxation time of the plasma must be much shorter than its expansion time,

which is typically in the microsecond and the spatial gradients in plasma temperature and

electron number density as estimated from diffusion length of atoms or ions during the relaxation

time, must be at least one order of magnitude shorter than the plasma dimension. Our

calculations show that obtained using Ge, Cu and Ba resonance transitions lie in the range

4-120 ns, which is much less than the plasma expansion time. Similarly, the diffusion length

for both samples was calculated as (0.1-1) x10-3

mm, whereas, the plasma diameter (d) was

estimated 1.5-2 mm (see for example Cristoforetti et al. [158] and El Sherbini et al. [38]). This


72

Figure 5-6: Boltzmann plots of the emission lines of Gd, Ge, Si, present in alloy and (b-d)

show the Boltzmann plots, built using Si emission lines of three solar cells.

implies that and hence the criterion is fulfilled for the plasmas to be in LTE in the

measurement interval.

In case of Gd/Ge/Si alloy and solar cells, the Boltzmann plots of Gd, Si and Ge lines and

Si emission lines from solar cells are shown in Fig. (5-6). Referring to Fig. (5-6a), the plasma

temperature extracted from the Boltzmann plots of Gd, Ge and Si lines (5600, 5900 and 5700 K)

are same within uncertainty. In the emission spectra of solar cells, only the Si emission lines

were enough to draw Boltzmann plot as shown in Fig. (5-6b-d). Plasma temperature calculated

from these plots was 5400, 5500 and 5400 K, which lies close to each other. This may be due to

the use of same laser ablation energy and optimized experimental conditions.


73

The electron number density in the plasma is required for LTE assessment and used in

Saha equation for concentration of ionic species. In the present work, we estimated the electron

number density in the temporal window of the measurements (1.6 s delay with 1 s equivalent

gate) from the Stark broadening of the Hα line. The Hα line and other emission lines have been

de-convoluted for instrumental broadening using several narrow emission lines emitted by a low-

pressure mercury argon lamp. The instrumental broadening 0.05 nm was subtracted from the

observed line profile as follows;

22

instrmeas

The electron number density in the Ge-Cu/Si alloy plasma has been evaluated from the

FWHM of Hα line as (1.44 ± 0.1) x1017

cm-3

. The electron number density was also determined

using various emission lines of Cu and Ge which lie in the range 1.3 ± 0.1 x1017

to 1.4 ± 0.1 x

1017

. Same electron number density values from Hα line and other emission lines implies that

self-absorption in the emission spectra is negligible [38]. Similarly, the electron number density

for the Ge-Ba/Si alloy was estimated using FWHM of Ge and Ba lines as (1.3 ± 0.1) x1017

and

that of Gd/Ge/Si alloy and solar cells were extracted as (1.24 ± 0.1) x1017

cm-3

, and (1.74 ± 0.1,

1.73 ± 0.1, 1.14 ± 0.1) x1017

cm-3

respectively. The validity of local thermodynamic equilibrium

for these plasmas has been verified using McWhirter criterion, relaxation time and plasma

diffusion length.

5.3.4 Elemental Concentration of Ge Alloys

The quantitative analysis of sample constituents has been carried out using calibration

free LIBS. The procedure of calibration free method for the quantitative analysis is described in

detail in first chapter. Briefly, the emitted line intensity from the optically thin and LTE plasma

can be expressed as follows:

eBline

eS

lineline

line TkEeTU

gAFCI

(5-1)

Here is the line integrated intensity, Cs is the species concentration, F is the

efficiency of the experimental setup. The spectroscopic parameters such as transition probability


74

( statistical weight ( , the partition function ( and the upper level energy of a

transition ( ) can be obtained from literature. Re-arranging Eq. (5-1) in the linear form as:

eSe

line

e

line

TUFC

kT

E

kTI

lnln

(5-2)

The intercept for each species is obtained from the linear fitting of data points in the

corresponding Boltzmann plot.

The elemental concentration of Ge/Cu/Si and Ge/Ba/Si alloys has been calculated using the

Calibration Free LIBS technique. The details of this technique are available in first chapter.

Referring to our previous work [163], the quantitative analysis using CF-LIBS technique require

plasma temperature and intercepts of all sample species extracted from Boltzmann plots. As an

example, the Boltzmann plots of Cu I, Cu II, Ge I, Ge II and Si I emission lines of Ge-Cu/Si

alloy are shown in Fig. (5-5). Similarly, the Boltzmann plots for the species in Ge-Ba/Si alloy

have been built and intercepts are obtained. The intercepts and plasma temperature are used to

get the concentration of all elements in both samples. In the present work, the concentration of

all detected elements in the emission spectra i.e. Ge, Cu, Si, Ge and Ba, have been determined as

listed in Table 5-1. Besides the major elements of the alloys, Li, Na, K and air constituents were

detected in trace quantity. Table 5-1 contains the elemental concentration of Ge-Cu/Si and Ge-

Ba/Si alloys in both weight and number percent.

The elemental concentration is also illustrated in Fig. (5-7), showing low concentration of Si in

the Ge-Cu/Si alloy, while much higher in the Ge-Ba/Si alloy. The inset in Fig. (5-7) represents

the concentration of air constituents and that of Li, K and Na in parts per million (ppm). In the

present work, we could not compare our results with any other technique. However, in our

recently published work on CF-LIBS analysis of Al-Si alloy [163], we used a reference sample

and the maximum deviation 2-3% of CF LIBS results from reference data was observed.


75

Table 5-1: Elemental composition of the germanium-based alloys.

Sample Elemental concentration

In weight % In ppm

Ge Cu Si Ba Li K Na H O N

Ge/Cu/Si alloy 89.90 10.02 0.07 - - - - 0.56 0.21 1.11

Ge/Ba/Si alloy 70.95 - 5.4 21.6 0.1 0.1 1.8 - - -

Sample

In number %

Ge Cu Si Ba Li K Na H O N

Ge/Cu/Si alloy 88.54 11.28 0.18 - - - - 0.004 0.0001 0.0006

Ge/Ba/Si alloy 68.7 - 13.5 11.1 1.0 0.2 5.5 - - -

Figure 5-7: Concentration of the elements present in Ge-Cu/Si and Ge-Ba/Si alloy. The

graph in the inset represents the concentration of trace elements in parts per million.


76

In other set of experiments, the elemental concentration of known Gd-Ge-Si alloy and three

unknown solar cells was determined by estimating plasma temperature (5700 K) and intercepts

of corresponding species from the linear fit of Boltzmann plots. However, the trace elements in a

sample usually have very few emissions line not enough to draw Boltzmann plots. To handle this

situation, a variant of CF-LIBS [147] could be used, which extract the intercepts from the basic

line intensity expression Eq. (1-27), rather than from the Boltzmann plot, provided that the

plasma temperature is known. Moreover, in CF-LIBS the ionic concentration is determined using

Saha equation, which requires the electron number density and concentration of neutral species.

The electron number density carries large uncertainty due to use of Stark broadening parameter.

Therefore, in order to improve the accuracy of CF-results, we proposed to extract intercept from

the ionic line using Eq. (1-27) and calculate the ionic concentration using Eq. (1-29).

With these strategies, the elemental concentration of Gd-Ge-Si alloy was determined by

estimating plasma temperature (5700 K) and intercepts of corresponding species from the linear

fit of Boltzmann plots. Since alloy spectra contain singly ionized lines of Ge and Si, therefore, its

contribution to overall elemental concentration was determined using Saha equation [32];

It is worth mention that in case of alloy the emission lines of Gd, Ge and Si were enough

to draw Boltzmann plots and get intercepts (see Fig. (5-6a). The elemental concentration of alloy

extracted “using intercepts from Boltzmann plots” was compared with the elemental

concentration determined “without using Boltzmann plots”. The comparison in Table 5-2 shows

that results of both approaches are almost comparable with some relative error. It is therefore

suggested that this approach is more suitable and that’s why it is extended to the analyses of

solar cells. In solar cells, only the emission lines of Si were sufficient to draw Boltzmann plot as

illustrated in Fig. (5-6b-d). However, the intercepts of rest of the elements in solar cells were

obtained using Eq. (1-27) and subsequently used for the determination of elemental

concentration. The inspection of table shows that silicon is the major constituent of all the solar

cell samples, because these solar cells are made of polycrystalline silicon, whereas other

elements are in trace quantity. These trace elements are divided into two groups, the dopants and

the contaminants. Dopants such as Phosphorous and Boron are added intentionally in solar cells,

as required to make the sunlight efficiently converted to electrical current, whereas, other

impurities such as Al, Fe, Ti, Ca, C and Cu etc. may come from raw materials or added during


77

the fabrication process. Sabation et al. [164] detected these impurities (B, Al, P. Ca, Ti, Cr, Mn,

Fe, Ni, Cu, Zn, Mo, Sn, W and P) in parts per million in MG-Si using XRF and ICP-MS. In

sample #1 and #2, the C and Ca were observed with reasonable concentration, however, in

sample # 3, Ca was in parts per million (ppm) but C was not present. The impurities In, Sn, Fe

and Pb were 4-50 ppm in sample # 3, but could not detected in Sample # 1 and 2. The

quantitative results for the three solar cell samples are listed in Table 5-3. Some other impurities

like K, Na, LI, Cu, Sr, Ag and Ba were identified in ultra-trace quantity. These impurities, in

crystalline structure decrease the conversion efficiency of solar cells and therefore their detection

and quantification is very much required for photovoltaic applications.

In CF-LIBS the ionic concentration is usually determined using Saha equation, which requires

the electron number density, carrying large uncertainty due to use of Stark broadening parameter.

Therefore, in the present work, the ionic concentration was directly determined using intercept,

extracted from the ionic line profile.

Results in Table 5-2 shows that the use of Boltzmann plot approach is more accurate, but

could not be applied to trace elements with less number of emission lines therefore impossible to

get the concentration of H, O, N and other trace elements. The “without Boltzmann plot”

approach was extended to the analysis of solar cells because in the emission spectra, very few

lines of trace impurities were detected and were insufficient to build Boltzmann plots.

Table 5-2: Elemental concentration determined using Calibration Free LIBS with and

without Boltzmann plots.

(Gd/Ge/Si

alloy)

Calibration Free Results (wt %)

Reference

values

% deviation

With

Boltzmann

plots

Without

Boltzmann plots

With

Boltzmann

plots

without

Boltzmann

plots

Gd 78.75 78.80 79.5 1 1

Ge 15.32 15.24 14.8 3.5 3

Si 5.92 5.95 5.7 3.8 4.4


78

Table 5-3: Elemental composition determined using Calibration Free LIBS without

constructing Boltzmann plots.

Elements Solar Cell # 1 Solar Cell # 2 Solar Cell # 3

Wt.% ppm Wt. % ppm Wt. % ppm

Si 99.78 98.09 99.45

Sb 0.54

C 0.17 1.6

Ca 0.04 0.3 29

In 53

Sn 21

Fe 4

Pb 1 3 < ppm

Al < ppm 2 < ppm

K < ppm < ppm 1

Na < ppm < ppm 1

Ti < ppm 1 < ppm

Li < ppm < ppm < ppm

Cr < ppm

Cu < ppm < ppm

Sr < ppm

Ag < ppm < ppm

Ba < ppm

79

Chapter 6

Conclusion and Future Plan 6

In this work, the capability of double pulse calibration free LIBS (DP-CF-LIBS) for

compositional analysis of alloys and solar cell samples have been studied, using the Q-switch

Nd:YAG laser and high resolution spectrometer.

In the initial part of the research work, the plasma of pure silicon was studied with the

help of plasma parameters at two wavelengths (1064 and 532 nm). Plasma temperature and

electron number density were studied as a function of laser irradiance, ambient pressure and

distance from the target surface. The results demonstrate higher values of electron temperature in

case of 1064 nm laser ablation, whereas, reversed behavior is observed for electron number

density. In the next set of experiments, CF-LIBS technique was employed for the quantitative

analysis of silicon, germanium and their alloys. The optimization of experimental parameters

such as laser energies, LTSD and gate delay time were very important for the accurate analysis.

For Al-Si alloy, at optimal conditions, the emission spectra was recorded and corrected for self-

absorption. The corrected emission intensities were used in Boltzmann and Saha Boltzmann

plots to calculate electron temperature. The fitting parameters extracted from the plots help to

determine the concentration of the species in the alloy. The results are obtained with 0.08-2%

relative standard deviation and up to 2.2% deviation from the reference data. In the next

experiment, double pulse plasma and CF-LIBS was incorporated to determine the stoichiometric

ratio of Ge-Cu/Si and Ge-Ba/Si alloys. The experimental parameters such as energy ratios, inter-

pulse separation and gate delay were optimized. LTE approximation was verified using

McWhirter criterion, excitation and ionization temperatures and by comparing the relaxation

time and diffusion length with plasma expansion time and plasma dimensions, respectively. The

plasma temperature was determined using Saha Boltzmann plot and electron number density was

Chapter 6: Conclusion and Future Plan

80

evaluated from the Stark broadened line profile of Hα line. Double-pulse measurement provides

higher sensitivity and allowed the detection of trace elements with improved limit of detection.

The conventional CF-LIBS technique requires Boltzmann plots for the elemental

concentration of all species in a sample; however, due to insufficient number of lines it is

difficult to build Boltzmann plot for trace elements and singly ionized species. A variant of CF-

LIBS technique was applied in which plasma temperature was determined with Boltzmann plot

of one species and the species concentration was determined without Boltzmann plots. The

concentration analysis of standard Gd-Ge-Si alloy of conventional and variant of CF-LIBS yield

same results with in uncertainty. The analysis has been further extended to three unknown

polycrystalline silicon solar cells using variant of CF-LIBS. The analysis yield silicon as 99.78,

98.09 and 99.45%, and trace impurities C, Ca, Sb, In, Sn, Ti, Al, and K were detected in parts

per million (ppm). The impurities in crystalline structure reduce the conversion efficiency of

solar cells and therefore their detection and quantification is very important for efficient

photovoltaic applications.

In future, we suggest the following work that can improve the scope of the work

presented in this thesis.

Double Pulse Orthogonal configuration could be used to improve the sensitivity and limit

of detection.

Portable system can be developed for the online qualitative and quantitative monitoring

of various samples.

Chemometrics analysis method for CF-LIBS can be established.

81

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