Measurement of Plasma Parameters in Laser-Induced Breakdown Spectroscopy Using Si-Lines

doi:10.4236/wjnse.2012.24028

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World Journal of Nano Science and Engineering, 2012, 2, 206-212

http://dx.doi.org/10.4236/wjnse.2012.24028 Published Online December 2012 (http://www.SciRP.org/journal/wjnse)

Measurement of Plasma Parameters in Laser-Induced

Breakdown Spectroscopy Using Si-Lines

Ashraf Mohmoud El Sherbini1,2, Abdel Aziz Saad Al Aamer1

1Department of Physics, Collage of Science, Al-Imam Muhammad Ibn Saud Islamic University (IMSIU), Al Riyadh, KSA

2Laboratory of Lasers and New Materials, Department of Physics, Faculty of Science, Cairo University, Giza, Egypt

Email: [email protected]

Received August 7, 2012; revised August 20, 2012; accepted September 6, 2012

ABSTRACT

The electron density and temperature of the laser induced silicon plasma were measured using two different methods.

The plasma was produced via the interaction of high peak power Nd:YAG laser at the fundamental wavelength of 1064

nm with a plane solid iron target contain small traces of silicon as an element of minor concentration. The lines from the

Si I at 288.15 nm and Si II-ionic lines at 413.08 and 634.71 nm were utilized to evaluate the plasma parameters. The

reference plasma parameters were measured utilizing the Hα-line at 656.27 nm appeared in the spectra under the same

condition. The electron density was measured utilizing the Stark broadening of the silicon lines and the temperature

from the standard Saha-Boltzmann plot method. The comparison between electron densities from different silicon lines

to that from the Hα-line reveals that the Si I-line at 288.15 nm contain some optical thickness while the Si II-ionic lines

were found to be free from this effect. The measurements were repeated at different delay times between the laser and

the camera in the range from 1 - 5 μsec. The electron density was found decreases from 2 × 1018 down to 4 × 1017 cm–3.

After correcting the spectral intensity at the Si I-line at 288.15 nm, the temperatures evaluated from the different meth-

ods were found in an excellent agreement and decreases from 1.25 down to 0.95 eV with delay time.

Keywords: Laser; Electron Density; Temperature; Plasma; Hα-Line

1. Introduction

The Laser-Induced Breakdown Spectroscopy (LIBS) te-

chnique is one of the potentially growing applied tech-

niques used in the field of elemental analysis, because of

its simplicity and non-contact nature [1-10]. Its basic

principle is based on exciting matter (solid, liquid or gas)

to plasma state through irradiation by high power laser

pulses. The plasma formed contains atoms and ions in

different excited states, free electrons and radiation. Un-

der the basic assumption that the emitted radiation is in-

fluenced by the properties of the plasma, hence, it gives a

detailed picture of the basic structure elements [9] and

different processes in the plasma [10]. The diagnostics of

the plasma can be done through the measurements of the

plasma electron density (ne) and temperature (Te). The

electron density in general, specifies the state of thermo-

dynamical equilibrium of the plasma, while the tempera-

ture determines the strength of the different distribution

functions describing the plasma state [11]. The optical

emission spectroscopy (OES) is the tool by which the

plasma can be diagnosed [11-13]. The measurement of

the electron density utilizing the Stark broadening effect

requires a line which is free from self absorption [11-14].

Self absorption occurs in general in any kind of system

capable of emitting radiation, such as homogeneous

plasma. Moreover, the formation of the plasma in LIBS

experiments in air shows, in general, a strong gradient of

temperature due to the cooling effect of the surrounding

air [15,16].

It was reported that the use the Hα-line at the wave-

length of 656.27 nm can grantee a precise measurement

of the electron density in LIBS experiments in open air,

since the condition on its optical thickness was examined

in a similar condition and verified to be optically thin

[14,15,17].

In principle, the self absorption process acting on the

strong emitted lines i.e. the lines emitted from the major

element in the target material in LIBS experiments

[16,18,19], and because of the passive action of this

process, one can’t use such spectral lines to determine

the electron temperature. Therefore, the lines that should

be considered in the measurement of the plasma parame-

ters must be chosen from the set of lines emitted from the

minor element in the target material [16] i.e. the silicon

lines in our case.

Historically, the relative concentration of Si II/Si I was

estimated utilizing the Saha-Boltzmann method [20]. In

A. M. EL SHERBINI, A. A. S. AL AAMER 207

this article, the time resolved images of the plume were

used to investigate the dynamics of the expanding plasma

plume, estimating the vapor pressure, vapor temperature,

velocity, and stopping distance of the plume [20]. A

Signal enhancements by factors of approximately 30 for

the Si I 288.16-nm line and 100 for the Al II 281.62-nm

line were observed with double pulses of the same total

energy [21]. This effect correlates with a substantial in-

crease in plasma temperature, with ionic lines and lines

having a higher excitation energy experiencing a larger

enhancement [21]. Laser-Induced Breakdown Spectros-

copy of silicon was performed using a nanosecond

pulsed, frequency doubled, Nd:YAG laser at wavelength

of 532 nm. Electron densities were determined from the

Stark broadening of the Si I 288.16 nm emission lines

and were found in the range from 6.91 × 1017 to 1.29 ×

1019 cm−3 at atmospheric pressure and 1.68 × 1017 to 3.02

× 1019 cm−3 under vacuum [22]. Milàn and Laserna [23]

performed diagnostics to silicon plasmas produced in air

at atmospheric pressure via interaction of 532 nm Nd:

YAG nanosecond laser. The plasma temperatures were

determined using the Boltzmann plot method while the

electron densities were determined from the Stark broad-

ening of the Si-line at 250.65 nm. Liu et al. [24] per-

formed spectroscopic analyses to silicon plasmas in-

duced by nanosecond Nd:YAG at 266 nm, at atmos-

pheric pressure and the plasma temperatures were deter-

mined utilizing the line-to-continuum ratio method.

Electron densities in the range of 1018 - 1019 cm−3 were

determined from the Stark broadening of the Si I at

288.16 nm line.

In this work we shall present the results of the meas-

urements of the plasma parameters (electron density and

temperatures) utilizing the silicon lines appeared during

the interaction of the Nd:YAG laser at the fundamental

wavelength of 1064 nm with plane solid iron target

which contains a small traces of silicon as well as from

the Hα-line at different delay times from 1 - 5 μsec and at

a fixed gate time of 2 μsec. The reference plasma pa-

rameters (density and temperatures) were saved using the

Hα-line. This piece of work emphasize on correction of

the spectral intensity from the silicon lines against the

effect of self absorption in order to evaluate a reliable

plasma temperature.

2. Experimental Setup

The experimental setup used in this paper is described in

previous articles [14,15]. A Q-switched Nd:YAG laser

(Quintal, model Brilliant B) was used at the emission

wavelength of 1.06 μm. The energy per pulse at the tar-

get surface was fixed at a level of 600 mJ. An absolutely

calibrated power-meter (Ophier, model 1z02165) was

used in measuring the fraction of the laser light reflected

from a quartz beam splitter to monitor the incident laser

energy. The laser was focused on the target by a quartz

lens of focal length of 10 cm. The target was a certified

Iron based alloy (type PANalytical B.V) with traces of Si

(1.16%) mounted on a precise xyz-stage at a distance of

9.7 cm to avoid a breakdown in air and arranged to pre-

sent a fresh polished surface at each laser shot.

The data acquired correspond to a single shot, aver-

aged three times under the same conditions for estimat-

ing the reproducibility margins at each data point. The

laser spot was measured at the target surface and gives a

circle of diameter of 1 mm because of the deflagration

effect and hence laser energy density of the order of 76

J/cm2 was calculated. The emitted spectra from the target

surface were acquired using an echelle spectrograph

(Catalina, model SE 200) equipped with a time gated and

high speed intensified charge-coupled device (ICCD)

camera (Andor, model iStar DH734-18F). A quartz opti-

cal fiber was positioned at a distance of 7 mm from the

axis of the laser and at 1.5 mm from the surface of the

target. The data was spatially integrated over a distance

of 1 mm from the target surface. The wavelength scale

was calibrated using a low pressure Hg-lamp (Ocean

optics). The instrumental bandwidth was measured from

the full width at half maximum (FWHM) of the Hg-lines

and was found on the average to be 0.12 ± 0.02 nm.

Identification of the different lines in the LIBS spectrum

was carried out using Spectrum Analyzer Software ver-

sion 1.6. The details of the setup can be found in Figure

1. The experimental setup was absolutely calibrated us-

ing a deuterium tungsten halogen lamp (type Ocean op-

tics, model DH 2000 CAL). The calibration curve in

Watt/au is shown in Figure 2, which enables us to de-

termine the emitted power at each line by direct com-

parison to the measured spectral intensity in the units of

au. The gain of the camera was kept at a constant level of

200. The gate time was adjusted at a gate time of 2 μsec,

while we have scanned the different delay times from 1

to 5 μsec to measure the temporal variation of the plasma

parameters at different delay times after the laser pulse.

2.1. Measurement of Electron Density

Spectroscopically, the electron number density in the

plasma can be measured through different suggested

methods namely; measurement of the optical refractivity

of the plasma [11], calculation of the principal quantum

number of the series limit [11-13], measurement of to

Stark profile of certain optically thin emission spectral

lines [13], the measurement of the absolute emission co-

efficient (intensity) of spectral line [13] and finally from

the measurement of the absolute emissivity of the con-

tinuum emission [13].

We shall concentrate on the measurement of the Stark

width of certain emitted spectral lines; especially the Hα-

lines appeared in our recorded spectra [14,15]. In principal,

A. M. EL SHERBINI, A. A. S. AL AAMER

208

Figure 1. The experimental setup.



cm 2,

















(2)

whereas, Δλ is the Lorentzian FWHM of the line, and ωs

is the Stark broadening parameter, that can be found in

the standard tables [25], Nr is the reference electron den-

sity which equal to 1016 (cm–3) for neural atoms and 1017

(cm–3) for singly charged ions [18,19]. In the last expres-

sion the ion impact broadening effect was neglected

[18,19]. In the above expressions, one should emphasize

that the lines used to evaluate the electron density should

be optically thin i.e. doesn’t subjected to absorption by

the plasma.

Figure 2. Absolute calibration curve over the spectrograph

wavelength region. 2.2. Measurement of Plasma Temperature

The measurement of the electron temperature can be

done through either of the following methods namely;

the relative intensity of two or more lines emerging from

the same kind of species and the same ionization stage

[11-13] or more general the Boltzmann plot [11-13]. The

wavelength separation of the lines used must be very

small in order to avoid the corrections against the relative

response of the detector, the upper excited state energy

separation should be as large as possible in order to get

precise results and the lines should be optically thin. The

temperature can be determined from the slope of the line

defined by the following expression;

one should properly matches the experimentally meas-

ured spectral line shape to the theoretically built profile

in a range of electron densities. At the best fitting, the

Lorentzian component of the measured FWHM can be

related to the concentration of the electrons in the plasma

[13]. In the special case of the hydrogen Hα-line, the

electron density can be related to the Lorentzian half

width at the half of the maximum Δλ1/2 through the rela-

tion [14];



312

cm8.02 10

















(1)

11122

22211

lnln 4π

hcN

IC AgE

CAgU kT





 









(3)

while, for atoms or ions other than hydrogen, the electron

density can be calculated, utilizing the relation [18,19]; whereas, I, λ, A, g are the spectral intensity, wavelength,

A. M. EL SHERBINI, A. A. S. AL AAMER 209

transition probability and statistical weight of the upper

state respectively. The subscript numbers indicates dif-

ferent lines. No, U

o are the population density and the

parathion function of the atom at temperature Te. The

constants h, c are the Planck constant and speed of light,

respectively. The lines intensities should be corrected by

the relative response factors C1,2, at the different emitted

wavelengths; these factors are saved from the absolute

calibration curve shown at Figure 2.

In order to enhance the precision of the measurement

of the temperature, one can use the second method which

suggesting the measurement of the relative intensity of

two or more lines from two emerging from a consecutive

ionization stages provided that these stages are in local

thermodynamical equilibrium (LTE). In that case the

Saha-Boltzmann equation should be used instead of

Equation (3) [11-13].

Moreover, the measurement of the absolute intensity

of an emitted spectral line can provide a precise means to

measure the electron temperature, provided that the elec-

tron density is known [13]. The following expression can

be used;



2πe

4π2

jj kT

hcA gmkT

msr h











 



(4)

whereas,



2nm

Ims







is the absolute spectral line intensity of the line in the

units of watt per unit m3 per unit solid angle in stridence

(emitted energy per unit time per unit area in a range

from λ to λ + Δλ per unit solid angle), Ne is the electron

density, that can be save from the Hα-line, Ei is the ioni-

zation energy of the atom ground state, and Ej is the ex-

citation energy of the upper emitting state. The rest of

symbols have their usual meaning.

It is worth noting that, the quantity



2nm

Ims







can be evaluated after calibrating the experimental setup

in an absolute way, as was done in our case.

2.3. Effect of the Self Absorption on the

Measured Plasma Parameters

The radiation emitted from the plasma may be subjected

to absorption by the cold region at the interface with

surrounding open air lay at the outer side region of the

plasma [16]. This absorption tends to destroy the shape

of the emitted lines i.e. the spectral line intensity de-

creases and the width (FWHM) is enlarged [13-16,18,19].

This effect can be best described by the coefficient of

self absorption (SA). The self absorption coefficient at

the line center (λo) can be defined as the ratio of the in-

tensity (counts per sec) of a spectral line subjected to self

absorption to that of the same line in the limit of negligi-

ble self absorption and can be calculated from [15]:



1e o

kl l

ole

oooo e

SA Ikl n









 









 







(5)

where Io (λo) is the spectral intensity of the line (counts

per sec) at the central wavelength (λo) in the limit of neg-

ligible self absorption (which often occurs in the very

small concentrations of the analyzed emitting atoms) and

I (λo) is the experimentally measured line height (counts

per sec) of the same line in the presence of self absorp-

tion [15]. Equation (5) indicates that the SA factor varies

from 1 in case of optically thin line to the limit of zero in

case of completely self absorbed line [15].

On the other hand, it was pointed out that the SA coef-

ficient can be expressed in terms of the ratio of the Lor-

entzian (FWHM) components of the line widths [15], Δλo

is the intrinsic FWHM of the Lorentzian component of

the spectral line in the case if the line is optically thin and

Δλl is the broadened FWHM of the Lorentzian compo-

nent of the same line because of the re-absorption proc-

ess which often occurs when the radiation passes the

plasma in its way to outside the plasma active volume.

Because of the process of re-absorption, a broadening of

the Lorentzian component of the line may be noticeable

[18,19]. The calculated electron density from utilizing

such broadened line of apparent width of Δλl will lead to

an apparent larger electron density value () in com-

parison to values evaluated from the Hα-line. By a direct

substitution in Equation (5) one can get an expression of

SA in terms of ratio of the electron densities evaluated

from the line under study to that from the Hα-line. Equa-

tion (5) shows that the SA coefficient can be expressed in

terms of the relative electron densities evaluated from the

line under investigation to that which is derived from the

reference Hα-line.

3. Results and Discussions

An example to a set of emitted spectra in the range from

200 to 1000 nm is shown in Figure 3, showing the strong

continuum component appeared under the spectrum

which decreases quickly with delay time. This continuum

component is originated from the free-free as well as

from the free-bound transitions [11-13]. The different Si

I, II-lines as well as Hα-line are clearly shown at the dif-

ferent delay times in the range from 1 - 5 μsec. We can

notice the decrease in the spectral intensity and the

widths of the different lines. This clear decrease in the

lines FWHM primarily indicates a decrease in the plasma

A. M. EL SHERBINI, A. A. S. AL AAMER

210

electron density, while the decrease in the spectral inten-

sity indicated a similar decrease in temperature.

The electron density from the Lorentzian FWHM of

the Hα-line was calculated utilizing Equation (1) with the

α1/2 parameter was given at Ref. [25]. At the best fitting

of the measured line shape to the theoretically calculated

Voigt shape one can extract the Lorentzian (ΔλStark)

component of the line FWHM. The theoretical line shape

was previously built through the convolution between the

different contributions to the lines FWHM taking into

account both of instrumental (ΔλInst ~ 0.12 nm) and the

Doppler (ΔλDopp ~ 0.04 nm) components. The results of

the measured electron densities utilizing the Hα-line as

well as from the Si I and Si II lines appeared in the same

spectra are shown in Figure 4, at different delay times in

the range from 1 - 5 μsec. The atomic constants used to

evaluate the electron densities from the silicon lines are

given in Table 1.

We can notice that the density calculated from the

ionic lines is very close to the densities which are calcu-

Figure 3. The recorded spectra at different delay times (1 - 5 μsec).

lated from the Hα-line under the same condition. This

indicated that these lines are optically thin (See predic-

tions of Equation (5)). On the other hand, the values of

the same density utilizing the spectral broadening of the

Si I at 288.15 nm shows a higher values than that from

the Hα-line. This result means that the line from the Si I

at 288.15 nm suffering from some optical thickness.

Moreover, this figure confirms that the coefficients of

self absorption are changing with delay time.

These coefficients of self absorption were calculated

using Equation (5) and the spectral line intensity was

corrected also using expression

Figure 4. The variation of the measured electron density

from different lines with delay time; open squares (Hα-line),

filled circles (Si I at 288.15 nm), open triangles (Si II at 413

nm) and the filled inverted triangles (Si II at 634 nm).

 

ISA





so as to give the values of the intensity Io (λo), as if, no

self absorption. Figure 5, Shows an example of the Saha-

Boltzmann plot after correcting the spectral line inten-

sity of the Si I at 288.15 nm against the effect of self ab-

sorption. We can notice that, after the application of the

correction process to the line of Si I at 288.15 nm, the

line joining the data points derived from the ionic silicon

lines well matches the data point from the neutral Si I at

288.15 nm.

Table 1. Atomic parameters of the Si I, II.

Element Wavelength

(nm)

Transition

probability

(sec–1)

Statistical

weight

Stark broadening

parameter

(nm)/Nr

Source

reference

Si I 288.15 1.89  108 3 0.00064633/1 

1016 11

Si II 413.08 1.42  108 8 0.0606/1  1017 11

Si II 634.71 7  107 4 0.09/1  1017 11

A. M. EL SHERBINI, A. A. S. AL AAMER 211

Figure 5. An example of the Saha-Boltzmann plot utilizing

the Silicon lines at a delay time of 2 μsec and gate time of 2

μsec.

Furthermore, we have used the absolute calibration in

order to evaluate the emission coefficients (intensities) at

the Hα-line in the units of (Watt/m2 nm Sr), and hence

with the help of Equation (4) the reference electron tem-

perature.

Figure 6 shows a comparison between temperatures

calculated using the absolute calibration at the Hα-line

(open squares) and the temperatures as measured from

the Saha-Boltzmann plot method. One can notice such a

close agreement between the measured electron tem-

peratures using the corrected spectral intensity of the Si I

at 288.15 nm and from the absolutely calibrated spectral

intensity of the Hα-line, and may indicate the quality of

the absolute calibration as well as the precision of the

correction of the spectral intensity against the effect of

self absorption.

4. Conclusion

The plasma parameters were measured to plasma cra-

tered via the interaction of Nd-YAG laser with a solid

target in air. The silicon lines, arose from target minor

concentration, were used to evaluate the plasma parame-

ters as well as the Hα-line. One line from the Si I at

288.15 nm was found to suffer from the effect of self

absorption that was repaired utilizing the Hα-line ap-

peared in the spectra. The temperature was calculated

using two different methods that can confirm one another.

One method is the ordinary Saha-Boltzmann plot after

correcting the Si I-line at 288.15 nm agonist self absorp-

tion and the other method using the absolute intensity

emitted from the Hα-line. A close agreement in the re-

sults of the different methods used in plasma diagnostics

shows that the spectral line intensity should be corrected

before be used in the measurement of temperature.

5. Acknowledgements

The experimental part of this work was conducted at the

Figure 6. The variation of the electron temperature with

delay time. The results of the different calculations are dem-

onstrated [circles are from the Saha-Boltzmann plot] and

[open squares from the absolute calibration].

Lab. of Lasers and New Materials, Physics Dep., Cairo

Univ., Egypt. The authors express their gratitude to the

valuable discussions with Prof. Th. M. El Sherbini and S.

H. Allam for their valuable discussions.

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