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Laser diagnostics for the electron density of helium low temperature plasmas using saturated absorption spectroscopy
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Laser diagnostics for the electron density of helium low temperature plasmas using saturated absorption spectroscopy Wonwook Lee a,b, Sungyong Shim b, Cha-Hwan Oh b,∗ a b
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea Department of Physics, Hanyang University, Seoul 04763, Korea
a r t i c l e
i n f o
Article history: Received 17 July 2019 Revised 2 September 2019 Accepted 23 September 2019 Available online 25 September 2019 Keywords: Helium Low temperature plasma Spectral line broadening Saturated absorption spectroscopy
a b s t r a c t Helium (He) low temperature plasma with an electron density higher than 1011 cm−3 was produced using an inductively coupled plasma source, and the electron density of this plasma was determined using a high-resolution laser spectroscopic technique. To remove the Doppler broadening which is the most dominant line broadening in low temperature plasmas, a saturated absorption spectroscopy system was configured. The Lamb dip was successfully separated from the Doppler broadening for the 21 S − 41 P transition of the He plasma using a high-resolution laser beam with a narrow spectral line width (below 1 MHz) at 396.5 nm. The estimated spectral line widths of natural broadening, van der Waals broadening, resonance broadening, and Stark broadening were 40.14 MHz, 0.93 MHz, 0.15 MHz, and 12.60 MHz, respectively, when the He gas pressure was 30 mTorr and 1 kW RF power was applied. The electron density of the He plasmas was determined to be ∼ 3 × 1011 cm−3 , which was comparable with those determined by a Langmuir probe and optical emission spectroscopy combined with a collisional-radiative model. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Atoms and ions in plasmas are suffered by collisions with another particle, local electric field by electron and another ion, and so on. These interactions cause various types of spectral line broadening such as natural broadening, Doppler broadening, resonance broadening, van der Waals broadening, and Stark broadening [1– 4]. Of these, the Stark broadening caused by charged particles is inevitable in plasmas. To understand Stark broadening in plasmas many of its fundamental characteristics have been investigated [5–9]. Two theoretical models, quasi-static approximation for ions [10–13] and impact approximation for electrons [13–21] has been suggested to explain Stark broadening. Theoretical research is still continuing, resulting in numerous algorithms to precisely calculate Stark broadening; such algorithms include PPP [22–24], MMM [25–29], QC-FFM [30,31], and FST [32–34]. Based on this research, Stark broadening has been successfully applied to astrophysical plasmas [15,35– 40] and atmospheric pressure plasmas [41–45]; it is widely used to determine the electron density of these plasmas because Stark broadening is larger than Doppler broadening in them. However, the spectral line broadenings, including Stark broadening, are much
∗
Corresponding author. E-mail address: [email protected] (C.-H. Oh).
https://doi.org/10.1016/j.jqsrt.2019.106674 0022-4073/© 2019 Elsevier Ltd. All rights reserved.
smaller than Doppler broadening in low temperature plasmas produced in a laboratory so the plasma diagnostics using Stark broadening are difficult to apply to low temperature plasmas. Recently, Zafar and co-workers [46] tried to measure the Stark broadening of helium (He) low temperature plasmas using Doppler-free spectroscopy. They extracted the electron density from the spectral data via fitting to a spectral model, but they did not separate the Lamb dip from the Doppler broadening. Additionally, they assumed that the He transition was a closed two-level system, and the low state did not experience any relaxation processes in the transitions between the exited states. In this study, we introduce various spectral line broadenings in low temperature plasmas and have calculated each spectral line broadening by considering all of the related states. Each spectral line broadening was evaluated in an He low temperature plasma, and the limit of detection (LOD) of the spectral line broadening in this type of plasma is discussed. We constructed an inductively coupled plasma (ICP) source to produce He low temperature plasma with an electron density higher than 1011 cm−3 , and also built a saturated absorption spectroscopy system to eliminate the Doppler broadening in the He plasma radiation. We successfully removed the Doppler broadening and separated the Lamb dip from it, and we also quantitatively determined the various spectral line broadenings, including Stark broadening, in the He low temperature plasmas. Based on the spectral line broadening without Doppler broadening, we determined the electron density of
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the resulting He low temperature plasmas and compared it with those determined by a Langmuir probe and optical emission spectroscopy combined with a collisional-radiative (CR) model. 2. Theory 2.1. Spectral line broadening The spectral line shape of plasma radiation is broadened in plasma. The theory of spectral line broadening has been investigated by many researchers and is described in detail in many texts [1–3]. In this section we introduce a simple expression of spectral line broadening and we discuss the characteristics of line broadening in He low temperature plasmas.
2.1.3. Van der Waals broadening, WV Among the interactions between particles in plasmas, the dipole interaction between radiators and the induced dipoles of atoms in a ground state creates the spectral line broadening of plasma radiation, known as van der Waals broadening. The approximate expression of FWHM of van der Waals broadening is given by [2–4,49,50]:
WV [Hz] = 2.452 × 10−1
α
9 = a30 2
R2j = 2.1.1. Natural broadening, Wn Natural broadening Wn is caused by the Heisenberg uncertainty relation, and the spectral line shape of natural broadening is Lorentzian because the line broadening is homogeneous broadening. Thus natural broadening is the minimum spectral line broadening that is measurable, and the full-width-half-maximum (FWHM) of the natural broadening Wn is given by [1–4]:
1 Wn = 2π
k
A pk +
Aqk ,
(1)
k
where Apk is the transition probability from the p-state to the kstate. Natural broadening is much smaller than Doppler broadening, so it cannot be measured until after the Doppler broadening is removed. Helium has two kinds of energy states, the singlet states (S = 0 ) and the triplet states (S = 1 ). The He transition lines in the visible range are those between the excited states, and the excited states have various possible optical transition paths. The n1 P state must be involved in optically allowed transitions in singlet states because of the selection rule. The transition probability of an n1 P state to the ground state is quite large [48], thus the natural broadenings of the singlet states are larger than the line broadenings of the triplet states because the optical transition of a triplet states to the ground state is forbidden. 2.1.2. Resonance broadening, WR Plasmas are composed of neutral particles, electrons, and ions that interact with each other. Some particles, known as perturbers, influence other particles such that the affected particles, known as radiators, produce plasma radiation. Among these interactions, a perturber may interact with the same species of radiator so that this interaction broadens the spectral line shape, which is called resonance broadening or self-broadening. When an upper or lower state of a radiator can resonantly transit to the ground state, resonance broadening occurs. The approximate expression for the FWHM of resonance broadening is given by [2–4]:
WR [Hz] = 2.581 × 10−3
gl λr FR N, gR
(2)
where gl and gR are the statistical weights of the ground state and the resonant level to the ground state, respectively. λr is the wavelength of the optical resonance line (cm), FR is the oscillator strength of the resonance line, and N is the number density of the ground state (cm−3 ). In He plasmas, transitions between triplet states are optically forbidden while those between the singlet states are optically allowed. Thus the resonance broadening in He plasmas occurs only between the singlet states.
n∗2 j 2
α R2
25 Tg 103 N, μ
(3)
2
3EH 4E2 p
,
(4)
5n∗2 j + 1 − 3l j l j + 1 ,
(5)
where Tg is the perturber’s temperature (K), μ is the reduced mass of the radiator-perturber system in atomic mass units (amu), N is the number density of the ground state (cm−3 ), α is the average polarizability of the neutral perturber, R2 is the difference between the values of the square of the coordinate vectors R2 of the radiating electrons in the excited state, (R2 = R2i − R2f ), EH is the hydrogen ionization energy, E2p is the energy of the first excited level of the perturber atom, n∗j is the effective principle quantum number, and lj is the orbital quantum number of the j state. In He plasmas, van der Waals broadening is linearly proportional to the density of the He pressure and is dependent on the He gas temperature. However, van der Waals broadening is almost constant in low temperature laboratory plasma because Tg and Tion are almost constant. 2.1.4. Stark broadening, WS The charged particles in the plasma interact with radiators, thus modifiying the plasma radiation such that the spectral line shape is broadened and shifted; this phenomenon is known as Stark broadening. Thus, Stark broadening should occur in plasmas, leading to many researchers investigating this phenomenon. Stark broadening is explained by the impact approximation for electrons and the quasi-static approximation for ions because of the mass difference between electrons and ions. The total Stark broadening for plasma radiation is the sum of the broadening of the electrons and ions. The approximate formula for the FWHM of total Stark broadening WS for He isolated transition lines is given by [3,9,35,51]: WS [Hz] =
2we c
λ
2 0
1
1
− 12
1 + 1.75 × 10−4 Ne4 Ai 1 − 0.068Ne6 Te
10−16 Ne
(6)
where we is the electron impact half width, Ai is the ion broadening parameter, Te is the electron temperature (K), λ0 is the observed wavelength (cm), c is the light speed (cm s−1 ), and Ne is electron density (cm−3 ). In Eq. (6), the effects on Stark broadening by electrons and ions are included. In various theories of Stark broadening [52,53], the change of its FWHM is small, so Eq. (6) is sufficient to determine the spectral line width of Stark broadening although various other codes and algorithms for Stark broadening can yield the exact spectral line profile. Stark broadening is mainly affected by the electron density and is almost linearly proportional to it, even though Stark broadening depends on the electron temperature. Thus, Stark broadening is a good candidate for determining the electron density of plasma. 2.1.5. Doppler broadening, WD In plasmas, radiators move fast in any direction and they produce plasma radiation. When an observer measures the plasma radiation, the measured frequency of the radiation is shifted because of the velocity difference between the radiator and the observer, the so called Doppler shift. The spectral line shape is broadened
W. Lee, S. Shim and C.-H. Oh / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106674
Fig. 1. Calculated spectral line broadening of (a) the 21 S − 41 P transition of 396.5nm, and (b) the 23 S − 33 P transition of 388.9 nm when the gas temperature was 315 K and the neutral gas density was 6.44 × 1014 cm−3 . The black, blue, green, orange, and gray lines represent Stark broadening, natural broadening, Doppler broadening, resonance broadening, and van der Waals broadening, respectively. The red line represents total spectral line broadening without Doppler broadening.
by this Doppler effect because of the velocity distribution of the radiators. The FHWM of Doppler broadening is given by [2–4]:
c T G WD [Hz] = 7.16 × 10 , λ0 M −7
(7)
where λ0 is the observed wavelength, TG is the temperature of the radiators (K), and M is the radiators’ mass (amu). Doppler broadening is a typical inhomogeneous broadening and its line shape is Gaussian, which sets it apart from homogeneous broadening such as natural broadening, Stark broadening, resonance broadening, and van der Waals broadening. 2.1.6. Spectral line broadening in helium plasmas Fig. 1 shows the calculated spectral line broadening of the He plasma in this study. The black line represents Stark broadening in Te = 20, 0 0 0 K and only Stark broadening is proportional to the electron density; the other broadenings do not depend on the electron density. Fig. 1(a) and (b) show the line broadenings of the 21 S − 41 P and 23 S − 33 P transitions, respectively. The Doppler broadenings in Fig. 1(a) and (b) are much larger than the other broadening; only Stark broadening is larger than the Doppler broadening, exhibiting Ne > 1014 cm−3 for the 21 S − 41 P transition and Ne > 1015 cm−3 for the 23 S − 33 P transition. When the electron density of plasmas is less than 1014 cm−3 , Doppler broadening is so predominant that other types of spectral line broadening cannot be measured because of it. Since the electron density of most low
3
temperature plasmas is less than 1013 cm−3 , the Stark broadening of He low temperature plasmas cannot be measured. Natural broadening of the singlet states in He atoms is much larger than the broadening of the triplet states as in Fig. 1(a) and (b). The natural broadening for the 21 S − 41 P transition in Fig. 1(a) was 40.14 MHz (λ = 21.05 fm ) in the frequency domain, and for the 23 S − 33 P transition in Fig. 1(a) it was 1.68 MHz (λ = 0.85 fm ). In the transition between singlet states, optical transition is allowed from the lower or upper state of the transition to the 11 S ground state. However, optical transition to the ground state is not possible from any of the triplet states of He because of the selection rule. The transition with the largest transition probability in the triplet states, 7.0703 × 107 s−1 , was 33 D − 23 P, which was smaller than that of the 11 S − 41 P transition [48]. Thus, the natural broadening of a triplet transition is always smaller than that of a singlet transition in visible wavelength. Resonance broadening did not occur here because, again, optical transition between the triplet state and the ground state is forbidden. Van der Waals broadening is proportional to the neutral density in both singlet and triplet states. In singlet states, natural broadening is much larger than van der Waals broadening and resonance broadening. However, in the transition between triplet states, van der Waals broadening is comparable to natural broadening, as shown in Fig. 2(b) and is not negligible. All particles in plasma always move fast, so Doppler broadening of plasma radiation is not inevitable. The LOD of the spectral line broadening is determined by Doppler broadening, thus the latter must be removed to measure homogeneous broadenings, including Stark broadening, in low temperature plasmas. Even though it is difficult to remove Doppler broadening from plasma radiation, nonlinear spectroscopy methods such as saturated absorption spectroscopy [47,54,55] have been developed to do so. In Fig. 1, all the spectral line broadenings except the Doppler broadening are homogeneous broadening, thus their line shapes are Lorentzian. Because the convolution of the Lorentz profiles is also the Lorentzian profile, the FWHM of the total spectral line broadening (without Doppler broadening) can be given by [3,50]:
WH = Wn + WS + WR + WV
(8)
The FWHM of the total homogeneous broadening is shown as the red line in Fig. 1 The red line is asymptotic to the natural broadening of the 21 S − 41 P transition and to the sum of the natural broadening and van der Waals broadening of the 23 S − 33 P transition as a function of the electron density; this is because van der Waals broadening is comparable to the natural broadening observed in the 23 S − 33 P transition. When the electron density of He plasmas is decreased to 1/10, the FWHM of the broadening also decreases to 1/10 because Stark broadening depends almost linearly on the electron density. Thus a high-resolution detection technique and instrument are needed to clarify broadenings in the low electron density of He plasmas. In this research, we used a light source with a spectral line width of 1 MHz. Because it was difficult to resolve less than 1 MHz experimentally, the LODs of the 396.5 nm and 388.9 nm transitions were 1 × 1011 cm−3 ; the other LODs of the He transitions are given in Table 1. When the 21 P − 51 D or 21 P − 61 D transition was adopted as a diagnostic transition, the LOD could be extended down to 1 × 1010 cm−3 . However, He atoms in the 21 P lower state can optically transit to the ground state, and the transition probability of the 21 P state was 1.7989 × 109 s−1 . The transition probability of the 21 P state was much larger than those of the upper states, and the natural broadening of the 21 P − 51 D and 21 P − 61 D transitions increased up to 288.7 MHz and 287.8 MHz, respectively. These natural broadenings were much larger than that of the 21 S − 41 P transition, 40.14 MHz. Additionally, the absorption signal for the 21 S − 41 P
4
W. Lee, S. Shim and C.-H. Oh / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106674 Table 1 Limit of diagnostics of electron density for He transition lines. Transition
Wavelength [nm]
LOD of Ne [cm−3 ]
23 S − 33 P 21 S − 41 P 23 P − 53 D 23 P − 53 S 21 P − 61 D 21 P − 51 D 21 P − 51 S 23 P − 43 D 23 P − 43 S 21 P − 41 D 21 S − 31 P 21 P − 41 S 23 P − 33 D 21 P − 31 D 23 P − 33 S 21 P − 31 P 23 S − 23 P
388.9 396.5 402.6 412.1 414.4 438.8 443.8 447.2 471.3 492.2 501.6 504.8 587.6 667.8 706.5 728.1 1083.0
1 × 1011 1 × 1011 1 × 1010 1 × 1010 1 × 1010 1 × 1010 1 × 1011 1 × 1011 1 × 1011 1 × 1011 1 × 1012 1 × 1011 1 × 1012 1 × 1012 1 × 1012 9 × 1011 1 × 1013
they are higher than the McWhirter criterion [61,62]. Recently, an He CR model with the a radiation trapping effect was developed and applied to various He plasmas [63–68]. The He CR model is the population model for neutral He and composes of the electron impact excitation/de-excitation process for all energy states of the neutral He atoms, the recombination process from He+ ions, and the spontaneous radiation. The rate equation of the He CR model with a radiation trapping effect is given by:
d N ( p) = Cqp Ne N (q ) dt q
1 − Fpq + C pq + S p + A pq Ne N ( p) N e q
p + [Fqp Ne + Aqp ]N (q ) q>p
+ + Fig. 2. Experimental setup of (a) the He plasma discharge system, and (b) the saturated absorption spectroscopy for He low temperature plasmas.
transition was larger than those for the transitions of 21 P − 51 D and 21 P − 61 D because the population density of the 21 S state was much larger than that of 21 P state. Thus it was easy to distinguish changes in the spectral line broadening when the metastable states of 21 S and 23 S were selected as the lower state. The transitions of 21 S − 41 P or 23 S − 33 P were good candidates for measuring the absorption spectra and the Doppler-free saturated absorption spectrum of the He plasma. 2.2. Helium collisional-radiative model The corona model is a simple model to diagnose low temperature plasma. In the corona model, only the electron impact excitation process from the ground state and the spontaneous radiative transition are allowed [56–58]. The corona model is used to determine the electron temperature of low temperature plasmas, and the model is valid in McWhilter criterion [58–60]. However, the electron density of our plasma source was more than 1011 cm−3 and was excluded from the McWhirter criterion. Thus, the corona model was not appropriate for determining the electron density of the He ICP in this study. The CR model for neutral He was developed to diagnose electron temperature and the electron density of He plasmas when
α p Ne + β p + β pd Ne N+
ρ (ν )[Bqp N (q ) − B pq N ( p)]
(9)
q
where Cpq and Fpq are the electron impact excitation and deexcitation rate coefficients from the p-state to the q-state, respectively, and α p , β p , β pd , and Sp are the rate coefficients of threebody recombination, radiative recombination, dielectronic recombination, and the electron-impact ionization for the p-state, respectively. The rate coefficients for the electron impact collisional process were calculated by the convolution of the cross section σ (Te ) with the Maxwellian electron energy distribution function [56,61,69]. Apq and Bpq are the Einstein A and B coefficients from the p-state to the q-state, respectively, ρ (ν ) is the spectral energy density of radiation at the transition frequency ν , N + is the population density of the ions, Ne is the electron density, and N(p) is the population density of the p-state. When the whole excited state (except for the ground state and metastable states) is in quasi-steady-state dN ( p)/dt = 0, the population density N(p) is given by:
N ( p) = r0,p Ne N + + r1,p Ne N (11 S ) + r2,p Ne N (21 S ) + r3,p Ne N (23 S ) + r4,p K31 P N (11 S ) + r5,p K41 P N (11 S )
(10)
where r0 , r1 , r2 , r3 , r4 , and r5 are the population rate coefficients. K31 P and K41 P are the radiative excitation rate coefficients for the radiation trapping effect. Detailed explanations are given in [63– 66]. In our He CR model, the atomic data for the electron impact excitation/de-excitation cross section, the radiative transition
W. Lee, S. Shim and C.-H. Oh / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106674
5
probability, and each recombination processes were adopted from [61,62,70–73]. From the atomic data and Eq. (10), the population density of the p-state and the intensities of the He transition lines were calculated. The electron density and electron temperature were determined by comparing the calculated transition line intensity ratio with the measured line intensity ratio. 3. Experiment To evaluate the suggested diagnostics, we constructed an ICP source that was able to produce He plasma with an electron density higher than 1 × 1011 cm−3 , as shown in Fig. 2. The vacuum system was composed of a quartz tube with a 20 mm inner diameter and 25 mm outer diameter, and the end of the tube was connected to a 15 cm stainless steel vacuum cube, which we called the probe chamber. Quartz viewports of 2.75 inch were installed in the cube to perform saturated absorption spectroscopy. An RF antenna was placed on the quartz tube and a Langmuir probe was installed in the probe chamber, which was 25 cm from the antenna. The gas pressure was controlled by a turbo molecular pump system, wherein the base pressure was less than 5 × 10−6 Torr. High purity (99.999%) He gas was injected into the vacuum system using a mass flow rate controller and the He gas was maintained at 20 − 40 mTorr. The number density of the neutral He atoms was calculated using the ideal gas law. To generate He plasma 13.56 MHz of RF power was applied to the Nagoya Type III RF antenna. We configured a saturated absorption spectroscopy setup to remove the Doppler broadening; the optical system was configured, as shown in Fig. 2. The system was composed of two laser beams, a pump beam with a strong light field and a probe beam with a weak light field [47,54,55,74]. When the two laser beams counterpropagated the saturated absorption signal, Doppler broadening could be measured. We selected the 21 S − 41 P transition instead of the 23 S − 33 P as the diagnostic transition line because the 21 S metastable state do not have any fine structure due to LS coupling. Thus, the natural broadening of the 21 S − 41 P transition was mainly determined by the transition probability of the 41 P state. An extra cavity laser diode (ECLD) system (TLB-6800-LN; Newfocus) oscillating at the wavelength of 396.5nm was used to measure the saturated absorption signal for the 21 S − 41 P transition of He atoms. The wavelength of the ECDL system was monitored using a wavelength meter (WS-U-1; High Finesse) and the frequency modulation range of the ECDL system was 19.4 GHz. The laser beam was separated into two laser beams using a beam splitter, resulting in a pump beam and a probe beam. The laser power of the strong pump beam was adjusted using a rotatable neutral density (ND) filter, and the weak probe beam was further separated into two laser beams using a 10 mm-thick quartz plate. The distance between the two separated probe beams was less than 5 mm. Probe beam 1 was used to measure the saturated absorption signal at photodiode 1 (PD1) while the frequency of the laser beam was modulated with a scan rate of 2 Hz. The power of the probe beam 1 was decreased to 9 μW by the ND filter. Probe beam 1 and the pump beam were aligned to overlap for at least 1 m along the length of the beam path. Thus, the cross angle of the two laser beams was less than 1/10 0 0 and the residual Doppler broadening could be neglected. The other weak beam, probe beam 2, was also simultaneously incident on the He plasma in parallel with probe beam 1 in order to measure the Doppler background signal at PD 2. The two probe beams were aligned to propagate near the Langmuir probe. The diameters of the pump beam and probe beams were ∼ 2.5 mm. The pump beam power was monitored by an optical power meter (LM2-UV; Coherent). The detected signals of PD1 and PD2 were recorded using a digital oscilloscope (DPO4104B; Tektronix). PD1
Fig. 3. (a) Saturated absorption signal of the He low temperature plasmas when laser power of 4.0 mW was incident on the He plasma. (b) The Lamb dip obtained from the saturated absorption signal. The black line is the measured signal and the red line is the Lorentzian fitted curve. The He gas pressure was 30 mTorr and 1 kW of RF power was applied to the antenna.
and PD2 were located far from the RF antenna to avoid RF noise and reduce the background radiation of the plasmas. To compare the measured results of saturated absorption spectroscopy with other methods, a Langmuir probe and an optical emission spectroscopy setup were also installed. The cylindrical Langmuir probe had a 1 mm diameter and 10 mm length and was aligned along the y axis as shown Fig. 2. The Langmuir probe measured the signal at five positions from the center of the probe chamber in 5 mm increments along the y axis up to 20 mm. An optical fiber with a 400 μm core diameter and 0.26 N.A was installed to collect the radiation of the He plasma and transfer it to a portable spectrometer (HR40 0 0; Oceanoptics) with ∼ 1 nm resolution. The optical fiber was placed at the front of the probe chamber on the off-laser axis and toward the end of the Langmuir probe. All of these optical components, i.e., the spectrometer, optical fiber, and viewport were relatively calibrated with a quartz tungsten halogen lamp (63976; ORIEL), which was designed for the calibrated light source. 4. Result and discussion Fig. 3 (a) shows the saturated absorption signal with the Lamb dip [47,54,55] measured by PD 1, where the Lamb dip signal was successfully measured at the center of the Doppler broadening signal. To obtain the exact Lamb dip, the Doppler background line profile had to be removed. The Lamb dip was definitely separated from the Doppler broadening by subtracting the Doppler back-
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Fig. 4. Laser power dependency of the spectral line width of the Lamb dip when the He gas pressure was 30 mTorr.
ground line profile measured by PD2 from the saturated absorption signal by PD1, as shown in Fig. 3(b). The saturated absorption signal had an overall Gaussian line shape and a Lorentzian line shape that appeared in the center of it. The Gaussian line shape was caused by Doppler broadening and the Lorentzian line shape was caused by all the homogeneous broadenings (natural broadening, Stark broadening, resonance broadening, and van der Waals broadening). The FWHM of the Gaussian line shape was 4.8 GHz (λ = 2.517 pm ) and the He gas temperature was determined to be 315 K by Eq. (7). The Gaussian line shape in Fig. 3(a) was removed by the signal measured by PD 2 so that the exact Lamb dip was obtained as shown in Fig. 3(b). The red line shows the fitted Lorentzian line shape, and the calculated line shape coincided well with the measured Lamb dip. The FWHM of the Lamb dip was 73 MHz (λ = 38.28 fm ). The FWHM represents the spectral line width of the total homogeneous broadening of Eq. (8). In addition to the line broadening, the power broadening should be removed to determine the homogeneous line broadenings, including the Stark broadening. Saturated absorption spectroscopy uses a strong light field, creating an additional spectral line broadening, known as power broadening. Power broadening is inevitable in laser spectroscopy, and the FWHM of laser power broadening ΓS is given by [47,54,55]:
ΓS =
WH 1 +
2
1 + S0
(11)
where WH is the total homogeneous line broadening in Eq. (8) and S0 is the saturation parameter. The saturation parameter is the ratio of the incident laser intensity to the saturation intensity [47,54,55], and the parameter is proportional to the incident laser power. To obtain the exact homogeneous line broadening without power broadening, the laser power dependency of the Lamb dip was evaluated as shown in Fig. 4 while the laser power was adjusted from 0.9 to 6.2 mW using the rotatable ND filter. When the laser power was reduced, the FWHM of the Lamb dip simultaneously decreased. The measured FWHM of the Lamb dip was fitted by Eq. (11) as the red line in Fig. 4. The intercept point between the fitted line and the y-axis represents the Lamb dip without power broadening, and the FWHM without the light field was determined to be 53.82 MHz (λ = 28.22 fm ). The other homogeneous broadenings without the light
Fig. 5. The squares, circles, and triangles respectively represent the electron densities found by the Langmuir probe, the He CR model, and the laser diagnostics using saturated absorption spectroscopy.
field were determined to be Wn = 40.14 MHz (λ = 21.05 fm ), WS = 12.60 MHz (λ = 6.61 fm ), WR = 0.15 MHz (λ = 0.08 fm ), and WV = 0.93 MHz (λ = 0.48 fm ). Using Eq. (8) and the red line in Fig. 1, the electron density was determined to be 3.85 × 1011 cm−3 when He gas pressure at 30 mTorr and 1kW RF power were applied. Fig. 5 shows the electron densities determined by the Langmuir probe, the CR model combined with optical emission spectroscopy [63,65–68], and the laser diagnostics using the saturated absorption spectroscopy when the He gas pressure changed from 20 mTorr to 40 mTorr while maintaining RF power of 1 kW. The electron densities found by the Langmuir probe were determined from the current-voltage characteristics [75,76] and the space-averaged electron densities for five positions ranged from 1.2 × 1011 cm−3 to 1.5 × 1011 cm−3 . To determine the electron density by the CR model, five line intensity ratios of 667.8 nm (31 D − 21 P ) / 728.1 nm (31 S − 21 P ), 706.5 nm (33 S − 23 P ) / 728.1 nm, 501.6 nm (31 P − 21 S ) / 728.1 nm, 492.2 nm (41 D − 21 P ) / 728.1 nm, and 587.6 nm (33 D − 23 P ) / 706.5 nm were selected. The electron densities by the He CR model were determined by comparing the measured line intensity ratios with the calculated line intensity ratios. The resulting electron densities ranged from 1.8 × 1011 cm−3 to 4.1 × 1011 cm−3 . The densities were within a factor of 2.7 of those found by the Langmuir probe and were consistent with previous reports [63–65,67,68]. Further, the electron density determined by the laser diagnostics changed from 3.4 × 1011 cm−3 to 4.3 × 1011 cm−3 when the He gas pressure changed. As shown in Fig. 5, these determined electron densities were larger (within a factor of 3) than those found by the Langmuir probe. In general, the electron density found by a Langmuir probe is usually underestimated and is within a factor of 2 − 2.5 of the corrected electron density [75,77–79]. The accuracy of the laser diagnostics is similar to that of Langmuir probe. In this study the increasing ratios of the electron density determined by the laser diagnostics were similar to those found by the Langmuir probe when the He gas pressured was increased. 5. Conclusion We investigated the spectral line broadening of He plasma radiation, including natural broadening, Doppler broadening, resonance broadening, van der Waals broadening, and Stark broadening. We calculated the spectral line broadening of an He low tem-
W. Lee, S. Shim and C.-H. Oh / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106674
perature plasmas and compared the line broadening of the transitions between the singlet states and the triplet states. The natural broadening of the transition between singlet states was larger than that between triplet states; this is because the transition probability of one of the states was much large. The LOD of the spectral line broadening for the He transition lines was determined when Doppler broadening was removed. To measure the Lamb dip, the optimal transition lines were evaluated such that the 21 S − 41 P transition line was selected. We constructed the He low temperature plasma source using an RF antenna. A saturated absorption spectroscopy system was configured to measure the spectral line broadening without Doppler broadening. The saturated absorption signal for the 21 S − 41 P transition was successfully measured and the Lamb dip was definitely separated from the Doppler broadening. The measured FWHM of the Doppler broadening was 4.8 GHz and the He gas temperature was evaluated to be 315 K. The FWHM of the Lamb dip was 73 MHz when the He gas pressure was 30 mTorr and 1 kW RF power was applied. To precisely determine the FHWM of the saturated absorption signal without power broadening, the Lamb dip was measured as a function of the laser power; the FWHM of the Lamb dip without a light field was thus determined to be 53.82 MHz and the electron density was determined to be 3.85 × 1011 cm−3 . The electron density determined by laser diagnostics was compared with the densities found by a Langmuir probe and a CR model. The accuracy of the laser diagnostics of finding the electron density and pressure dependence was in the same level with another diagnostics in the He gas pressure range from 20 to 40 mTorr. Acknowledgements
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