IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 3, MARCH 2014 813 Interpretations of Langmuir Probe Data for Positive Ion Number Density of N2O DC Plasma Discharge Jennet Rodríguez Legorreta, Farook Bashir Yousif, Member, IEEE, Elizabeth Beatriz Fuentes, Federico Vázquez, and Horacio Martínez Valencia Abstract— Electronegativity of N2O dc plasma discharge was investigated by evaluation of the positive ion number density and electron number density. The positive ion number density was obtained using the positive ion current part from recorded I–V characteristic curves. Results obtained employing the Allen-Boyd- Reynolds, current balance, and orbital motion limited methods were found to be compatible, and the floating potential (FP) method was found to be a magnitude of higher order. Electron temperature and number density were also obtained for N2O by the exponentially rising electron current of the I–V curves. The FP method was also employed by taking advantage of the positive ion current, and part of the I–V characteristic curves was also used in the evaluation of the electron temperature. Electron energy distribution function was evaluated and used to obtain the electron number density and temperature. Electronegativity of the N2O was deduced using the measured data of electron and negative ion number densities. Index Terms— Electron temperature, electron energy distri- bution function (EEDF), electronegative plasma, positive and negative ion number density. I. INTRODUCTION ELECTRONEGATIVE gases such as nitrous oxide havenumerous applications in chemistry, medicine, and tech- nology. Electron interactions with N2O are important for atmospheric chemistry, for being a greenhouse gas with approximately 200 years of permanence in stratosphere [1], [2]. Equally it is one of the harmful global warming gases following carbon dioxide and methane with global warming potential of 310, identifying it as an ozone depleting gas in the upper atmosphere. N2O is a primary source of stratospheric nitrogen oxides, referring specifically to NO and NO2. Both of which are ozone-depleting gases. Although the ozone- depleting potential (ODP) of N2O (0.017) is lower than that of the chlorofluorocarbons (because only 10% of N2O is converted into nitrogen oxides), N2O emission is reported to Manuscript received March 16, 2013; revised August 24, 2013 and January 29, 2014; accepted January 30, 2014. Date of publication February 18, 2014; date of current version March 6, 2014. This work was supported in part by Consejo Nacional de Ciencia y Tecnología under Contract 41072-F, in part by CONACyT under Grant 128714, in part by DGAPA under Grant 105010, in part by the Programa de Mejoramiento del Profesorado, in part by the Programa Integral de Fortalecimiento Institucional-2, and in part by the CONACyT under Project 43643/A-1. J. R. Legorreta, F. B. Yousif, and F. Vázquez are with the Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca 62210, México (e-mail:
[email protected];
[email protected]). E. B. Fuentes is with the Facultad de Ciencias, Cuernavaca 62251, México. H. M. Valencia is with the Centro de Cieincias Fisicas, Cuernavaca 62251, México (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2014.2304417 be the only largest ODP-weighted emission and is expected to be the largest for this century. Therefore, decomposition of N2O is essential through electrical discharges for environmen- tal reasons. It is considered as an alternative to gases such as SF6, yet little is known about its characteristics. Nitrous oxide is considered to be a weakly electronegative (weak polar) molecule [3]. Thus, it has been considered as a candidate for the investigation of its electronegativity in this paper. Few experiments have been performed with respect to N2O, mainly by beam techniques with total cross sections measurements [4]–[8]. However, electrical characteristics and emission spectroscopy, as well as electron temperature and number density of this gas were investigated previously in this laboratory [9], [10]. Yet to the best of our knowledge there has been no reported data on the electronegativity of this gas or the positive ion number density. On the other hand, there has been a growing interest in electronegative plasma reactors [11]–[13] as well as with various methods of the negative ion density determination [14]–[18] and equally in the importance of several diagnostic tools and methods. Moreover, the negative ion production in the plasma influences film formation [19], [20]. In addition to positive ions and electrons, negative ions are formed owing to attachment of electrons to neutral atoms and molecules, as well as dissociative attachment. Therefore, in the electronegative plasma as in N2O, the plasma is formed of positive ions n+, negative ions n−, and electrons ne. The quasineutrality condition is required to satisfy the charge balance n+ = ne + n− [21] at the plasma bulk where the potential is negligible and with the electronegativity defined as α = n−/ne. The n+, and n− are the sum of all possible positive and negative ions, respectively. During this paper, several methods were employed in the evaluation of the positive ion density. These are: the Bohm, the Allen-Boyd-Reynolds (ABR), the orbital motion limited (OML), the current balance (CB), and the floating potential (FP) methods. All of these are based on taking advantage of the positive ion saturation current of the I–V curve. Therefore, the aim of this paper in part is to test the validity of each of the four methods in the determination of the positive ion density. II. EXPERIMENTAL APPARATUS Details and diagram of the experimental apparatus are found in [10]. The cathode cylinder is of stainless steel and of 7 cm in length and was reduced in diameter to 3.5 cm, and the anode is a 1.5-mm diameter stainless steel rode and of 7-cm length. 0093-3813 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 814 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 3, MARCH 2014 Fig. 1. I–V curve plotted at 12 W of power and 75 mTorr of pressure, with electron exponential and saturation parts, line fitted. Gas was permitted into the reactor at a constant flow through a pulsed valve of 0.1-mm orifice and with a large opening time, whereas a gate valve to a turbo pump was partially opened for constant flow environment. The base pressure obtained with no gas and no discharge was 10−4 mTorr. Discharge was initiated employing 500 V and 50 mA dc power supply. I–V curves were recorded as a function of discharge pressure and constant power for a cylindrical probe of 3-mm length and 0.13-mm diameter. The probe bias voltage was scanned between −40 to +40 V while recording the current. The probe was positioned at a mid distance between cathode and anode and protruding 3 mm into the plasma. Several averaged ascending scans were made for each final I–V curve. The standard deviation of the scans was within 5%. III. RESULTS AND ANALYSIS Example of I–V characteristics curve measurements is plotted in a linear and natural logarithmic scale as shown in Fig. 1, at 12 W of power and 75-mTorr pressure. The exponential part of the curve represents the contribution of electrons and negative ions. Linear fits were made for both, the electron saturation region and the exponential region of the curve were identified as the inverse tempera- ture region, with their intersection occurring at the plasma potential Vp. As seen from Fig. 1, the floating potential is shifted to the negative side of the bias potential at about 5.25 V. This behavior has been reported previously [22]. It is related to the presence of negative ions which reduces the value of the floating potential. This can be understood by the decrease in the floating potential corresponding to the decrease in the average temperature of the population of negative species. The variation of ln IP as a function of probe voltage V is linear in the region below plasma potential with the slope yielding the electron temperature Te d ln Ip dV = 1 Te Fig. 2. (a) Example of an I–V curve scan, (b) first derivative dI /dV , and (c) second derivative dI /dV 2, at 75 mTorr and 9 W of power. from which the electron number density is obtained from the expression ne = Ie,sat√ kTe 2πme A pe where me is the electron mass and A p is the cylindrical probe tip area. The electron number density is also determined by evaluating the electron energy distribution function (EEDF) following the methods of Druyvesteyn [23]. Druyvesteyn method is based on the extension of Langmuir and Mott-Smith probe theory [24], which allowed the determina- tion of the EEDF from the following the expression: N(∈) = 2 Ae [ 2me ∈ e ]1/2 d2 I dV 2 . (1) The associated electron energy probability function EEPF is found from P(∈) = 2 Ae [ 2me e ]1/2 d2 I dV 2 (2) where V is the probe voltage, ∈ = (Vp − V ) is the probe voltage with respect to plasma potential, A is the probe area, d2 I/dV 2 is the second derivative of the characteristic curve, e is the electron charge, and me is the electron mass. Hence, the electron density is obtained from the integral of P(∈) ne = ∞∫ 0 P(∈)d∈. (3) The electron temperature is given as Te = 2 3 (∈) = 2 3ne ∞∫ 0 ∈ P(∈)d ∈. (4) YOUSIF et al.: INTERPRETATIONS OF LANGMUIR PROBE DATA 815 Fig. 3. EEDF obtained from the second derivative of Fig. 2, and the measured plasma potential. Fig. 4. Electron temperature obtained by different methods (EEDF, slope, and FP methods) as a function of pressure at 9 W of power. First d I/dV is calculated for the raw data of the I–V curve of Fig. 2(a) and plotted as a function of the probe voltage as shown in Fig. 2(b). The maxima of Fig. 2(b), gives the plasma potential. Furthermore, d2 I/dV 2 is obtained and plotted as a function of probe voltage as in Fig. 2(c). The EEDF is evaluated from d2 I/dV 2 and the measured plasma potential and is shown in Fig. 3. Integrating the EEDF according to (3) gives ne, and Te is obtained from (4). The electron temperature that was measured using the expo- nentially rising electron current (slope method), the positive ion current parts of the I–V characteristic curves employing the FP method [25] and the EEDF method are shown in Fig. 4 as a function of pressure. The FP method [25] describes the procedure as follows. The ion part of the I–V characteristics raised to the three- fourths power and plotted as a function of probe voltage Vpr. The ion current is then calculated from the straight line fit to I 4/3i , then subtracted from the total current to obtain Ie. Consequently, Ie is plotted semilogarithmically as a function of probe voltage. Fitting a straight line to the resulting curve yields the electron temperature K Te in eV. The electron number density as a function of pressure employing the exponentially rising electron current (slope method) and the EEDF method are shown in Fig. 5. Fig. 5. Electron number density obtained employing the EEDF and the slope methods as a function of pressure. Electron temperature employing the EEDF method is about 40% higher than the slop method and 20% higher than FP method at low discharge pressure. This difference decreases as the pressure is increased and all of the three methods lead to the same electron temperature at about 450 mTorr. However, the electron number density obtained using the slope and EEDF methods are in reasonable agreement over the entire pressure range as seen in Fig. 5. The drop in the Te as a function of pressure can be explained that the lower Te is needed to compensate for a higher number density at higher pressures as the energy losses is increased owing to higher collisional frequency. The decrease in the electron number density as a function of pressure as seen in Fig. 5 is due to the fact that an increase in gas pressure leads to the cooling effect of the plasma that eventually decreases the saturation current and the electron number density [26]. Simi- lar decrease in ne as a function of pressure was reported [27], where they employed the symmetric double Langmuir probe on inductively coupled RF-plasma. Both, positive and negative ions are produced in the plasma discharge. O− is the only negative ion produced [3] through the dissociative attachment of low-energy electrons to N2O via the reaction e + N2O → N2O− → N2 + O−. NO+ is the dominant positive ion [27] produced via the reactions e + N2O → N2O∗ + e N2O∗ → N2O+(X2�)+ e N2O +(X2�) → NO+(X1�+)+ N(4 S). The NO+ ions are in their ground state, which is confirmed by the absence of any emission lines in the emission spectra of N2O [10]. To evaluate the positive ion number density, several methods were employed. These are the OML, the Bohm, the CB, and the FP methods, all of which used the positive ion part of the I–V characteristic curves. The measured electron density is low; therefore, the Debye ′ s length is larger than the probe radius (0.065 mm) and the sheath thickness. Thus, all of 816 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 3, MARCH 2014 the proposed methods are, in principal, appropriate in the determination of the positive ion number density. Details of these methods are described in [25] and [28] and briefly outlined here. The OML theory is applied for low-density plasmas with a thick sheath and the positive ion current that is mainly due to NO+ is given as Ii = n+eA p √ kTe 2πM+ 2 π [ e(Vp − Vpr ) kTe ] 1 2 . (5) From the positive ion saturation, a plot of I 2i = AVpr + B can be made and the positive ion density can be determined from the slope. The OML theory leads to the Bohm method, when the effective collecting area of the probe tends to zero, leading to Ii (V ) = 0.4qn0S √ 2qTe M+ . (6) In the CB method, positive and negative currents are at balance (zero crossing in the I–V curve). Defining the sheath area at the floating potential as A f , and the modified Bohm flux to be �s = 0.6n+cs , then 0.6n+A f cs = ne A p √ kTe 2πme e−e�V/kTe (7) where A f is estimated from either the Child–langmuir (CL) law or the ABR theory and �V is the voltage difference between the plasma potential and the floating potential. Thus, the experimental data of Vp , V f , ne, Te and ion mass can be used to obtain the positive ion number density n+. Details of the FP method for evaluating the positive ion number density were reported in [25] and briefly reported here. From an I–V curve, dI/dV is taken, which gives the plasma potential Vp. The ion part of the I–V curve is raised to the 4/3 power and plotted against probe voltage Vpr. Following that a straight line is fitted to the ion part of the curve. Extrapolating to V f where Ii = Ie = 0 gives an estimate of Ii (V f ). Following that, the ion current is calculated from the straight line fit to I 4/3i . To find ni from Ii (V f ), we assume the sheath thickness given by CL formula as follows: d = 1 3 √ 2 α0 (2η f ) 3/4λD = 1.918η3/4f λD (8) where λD ≡ (ε0kTe/ne2)1/2 (9) is the Debye’s length. Here sheath radius is the sum of d and the probe radius Rp because Ii = α0n Ascs . Therefore, from the last two equations, and as Ii = α0n Ascs , and for a probe length L, we get n = Ni (CL) = Ii (V f )/2π(Rp + d)Lα0cs . (10) Equations (9) and (10) form a quadratic equation for n−1/2, whose solution lead to positive ion density as n = {[ −B + (B2 + 4AC)1/2 ]/ 2A }2 where A = Rp , B = η3/4f (ε0 K Te/e2)1/2 and C = Ii (V f )/2πLα0cs . The solution of Poisson equations can be extended to infinity; therefore, the ABR theory that neglects orbiting can be applied as it was modified [16] for cylindrical probes 1 r ∂ ∂r ( r ∂V ∂r ) = e ε0 (ne − ni ) where ne = n0eeV/kTe = n0e−η. As n → n0 and V → 0 when r → ∞, the velocity of the positive ions is vi = (−2eV/M)1/2 = (2η)1/2cs and taking ξ = r/λD then ni = Ii/vi 2πr = Ii 2πrCs (2η)−1/2. Resulting in (8) to take the form ∂ ∂ξ ( ξ ∂η ∂ξ ) = Iiξ 2πrn0cs (2η)−1/2 − ξe−η = Ii 2πn0λDcs (2η)−1/2 − ξe−η. (11) Putting the normalized ion current J to be J ≡ Ii/23/2πn0λDcs . Therefore, in terms of J , the Poisson equation becomes ∂ ∂ξ ( ξ ∂η ∂ξ ) = Jη− 12 − ξe−η. (12) For each value of J , the last equation can be solved for η(ξ) for all ξ . The probe radius ξp at floating potential can be found from the condition Ii = Ie at the probe surface. From the Bohm criteria, we have Ii = 2πRsα0n0cs where α0(Rs/Rp) = √ 2J/ξp = α. (13) By putting α = α0(Rs/Rp) where α is for the modified Bohm criteria for cylindrical probe, then Ii = 2πRpαn0cs (14) where 2πRpα is the effective collision area of the probe. Then Ni(ABR) = Ii(Vf ) 2πRpcsα = Ii(Vf )ξp 2πRpcs √ 2J . (15) From Lafamboise curves we have 1 J 4 = 1 (AηB)4 + 1 (CηD)4 (16) where for the ABR method A,C = aξb + cξd and B, D = a + bInξ + c(Inξ)2. The coefficients in Table I were used to obtain J . Once J is found, then α can be obtained from (13), leading to Ii from (14) which in turn can be used to obtain Ni from (15). YOUSIF et al.: INTERPRETATIONS OF LANGMUIR PROBE DATA 817 TABLE I COEFFICIENTS USED TO OBTAIN J Fig. 6. Comparison of the positive ion number density obtained by several different methods (FP, Bohm, OML, ABR and CB) within the pressure range of 75–450 mTorr. The results obtained from employing the above-mentioned methods for n+ are shown in Fig. 6. The negative ion density can be obtained from the direct application of the charge balance equation. Beside the standard deviation of the scans that was within 5%, all of the above-mentioned methods in obtaining the positive ion number density as well as the electron temperature relied on the recorded I–V curves. Measurements of I and V would imply additional instrumental errors in both voltage and current measurements. Both are estimated by manufacturers to be less than 1%. Furthermore, an additional error to be considered is due to probe diameter measurements, which was also less than 1%. Therefore, for all the data reported in this paper, an upper limit error bars of ±10% were included. Our results for n+ for the FP method following the method of [25], was found to be higher than those of ABR, CB, Bohm criteria and OML by about on order of magnitude, within our pressure range of 75–450 mTorr. As for the Bohm criteria method, the equation Iis = 0.6eAn+cs for plane probe was applied. The concern in elec- tronegative plasma is that how much is the difference between the actual positive ion saturation current and Iis = 0.6eAn+cs . Here, assuming that the positive ions at the sheath edge are at Bohm speed cs , where A is the sheath area. However, since the measured ion current by cylindrical probe does not saturate and the contribution from negative ions is difficult to estimate, the application of the above mentioned equation at plasma potential may not be accurate. The results obtained employing this method are between one and three times higher than those Fig. 7. Electronegativity (n−/ne) as a function of pressure. obtained employing ABR, CB, and OML methods as seen in Fig. 6. Possible reason is that the ion collection area for cylindrical probe depends on the sheath radius Rsh which is not known a priori. Thus, there is no need for the artifice of a sharp sheath edge as in the plane probe that is used in the Bohm method. The measured electronegativity given as n−/ne as a function of pressure is shown in Fig. 7. It is found to be weakly dependent of the increase in pressure with the FP method giving the highest electronegativity. As it is assumed that the sheath structure and the motion of positive ions within the presheath are modified when the negative ions are present. Therefore, as the negative ion density increases reaching critical negative ion to electron ratio of 2, the Bohm criteria is modified [29]. It would affect the determination of the positive ion density. Akihiro [29] showed that for n−/ne > 2, as it is the case with our results for the FP method, the positive ion flow toward the probe gains the ion sound speed in the presence of negative ions, which results in the formation of a potential barrier confining the negative ions in the plasma core, thus a positive space charge is to be formed. As the positive ions flow is further accelerated toward the probe, the emerged positive space charge decreases. Thus allowing positive ion speed to reach the Bohm speed before the positive space charge decreases down to zero, and again the positive space charge begins to increase forming a stable ion sheath leading the electronegative plasma core to be directly connected to the positive ion sheath resulting in an accurate positive ion density determination. On the other hand, the negative ions have a low temperature, that is, about one order of magnitude lower than the electron temperature in plasmas of low pressure could be held back by the potential barrier. It was also confirmed in the investigation [30] of the presheath characteristics under the influence of negative ions that owing to the potential drop from the bulk plasma to the sheath-presheath edge, the negative ions will be repelled from this region and hence the negative ion density in this region will be different from that of the bulk plasma. Bailung et al. [30] also verified that the negative ion den- sity at the sheath edge varies nonlinearly with temperature ratio T−/Te. 818 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 3, MARCH 2014 IV. CONCLUSION Electron temperature and number density as a function of pressure were found to agree very well when obtained from the exponentially rising electron part of the I–V curves or from using the positive ion current part of the I–V curves employing the FP method for N2O plasma. The electron temperature and density obtained by evaluating the EEDF were found to be higher than those obtained from the slope and FP methods. The ABR, OML, CB, Bohm, and FP methods were also used to obtain the positive ion density and hence the negative ion density. The floating potential method was found to be more than one order of magnitude higher than the other methods. All of these methods were found to be weakly dependent on the increase in discharge pressure. The Bohm criteria method which is initially formulated for the plane probe was found to give higher results than those by the OML, ABR, and CB methods. 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Jennet Rodríguez Legorreta is currently pursuing the Ph.D. degree in atomic, molecular, and optical physics from the Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Cuernavaca, Mex- ico. Farook Bashir Yousif (M’13) received the M.Sc. and Ph.D. degrees in experimental atomic and molecular physics from the Queen’s University of Belfast, Belfast, U.K., in 1983 and 1985, respec- tively. He is currently a Full Faculty Professor with the Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Cuernavaca, Mexico, and leads a Research Laboratory in molecular, and optical physics. His current research interests include high- resolution mass spectroscopy, molecular dynamics, photodissociation, photoionization, and cold-temperature plasma physics. YOUSIF et al.: INTERPRETATIONS OF LANGMUIR PROBE DATA 819 Elizabeth Beatriz Fuentes, photograph and biography not available at the time of publication. Federico Vázquez received the M.Sc. and Ph.D. degrees in physics from Universidad Nacional Autonoma de Mexico, Mexico city, Mexico, in 1990 and 1996, respectively. He is a member with the Mexican Academy of Sciences, Mexico, and currently a Full Faculty Professor with the Facultad de Ciencias, Universi- dad Autonoma del Estado de Morelos, Mexico city, Mexico, and leads research in thermodynamics and statistical physics. His current research interests include irreversibility and stochastic phenomena in fusion and cold-temperature plasmas, photonic crystals, thermoelectric materials, and complex fluids. Horacio Martínez Valencia received the Ph.D. degree from Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM), México City, México, in 1987. He is currently a Researcher with the Instituto de Ciencias Fisicas, UNAM. He leads the Spectroscopy Laboratory, Instituto de Ciencias Fisicas. His current research interests include basic plasma phenom- ena, low-temperature plasma, plasma surface inter- actions, spectroscopy of cold plasma, plasma diag- nostics, and atomic, molecular, and optical physics. /ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 600 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 400 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description > >> setdistillerparams > setpagedevice