World Journal of Nano Science and Engineering, 2012, 2, 206-212 Published Online December 2012 (
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
Received August 7, 2012; revised August 20, 2012; accepted September 6, 2012
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
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
opyright © 2012 SciRes. WJNSE
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 cm3 at atmospheric pressure and 1.68 × 1017 to 3.02
× 1019 cm3 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 cm3 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,
Copyright © 2012 SciRes. WJNSE
Copyright © 2012 SciRes. WJNSE
Figure 1. The experimental setup.
cm 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];
cm8.02 10
lnln 4π
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,
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;
jj kT
hcA gmkT
msr h
 
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
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
oooo e
SA Ikl n
 
 
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
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Copyright © 2012 SciRes. WJNSE
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).
 
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
Stark broadening
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
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
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-
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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