langmuir double probe rf plasma compensation using simulation method

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Computer Physics Communications 185 (2014) 350–356

Contents lists available at ScienceDirect

Computer Physics Communications

journal homepage: www.elsevier.com/locate/cpc

Langmuir probe RF plasma compensation using a simulation method✩

A.A. Azooz ∗, Y.A. Al- Jawaady, Z.T. AliDepartment of Physics, College of Science, Mosul University, Mosul, Iraq

a r t i c l e i n f o

Article history:Received 11 March 2013Received in revised form2 September 2013Accepted 4 September 2013Available online 12 September 2013

Keywords:RF plasma compensationLangmuir probeEEDF

a b s t r a c t

The problem of Langmuir probe data deformation due to RF pickup by the probe is treated througha computer simulation method. It is pointed out that proper RF compensations can be obtained bytreatment of the Langmuir probe raw data through the use of computer software. It is demonstrated thatcorrect, RF unaffected probe I–V characteristics can be accurately reproduced from the RF contaminateddata. This eliminates the need for the use of any filters or other hardware procedures. User friendlymatlabbased software is presented. The software automatically retrieves the correct RF I–V characteristicsfor single Langmuir probe data which consequently allows for proper evaluation of plasma parameterssuch as the plasma electron temperature, electron number density and the electron energy distributionfunction (EEDF)

Program summary

Program title: RF CompensationCatalogue identifier: AEQR_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEQR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Copyright (c) 2009, aasim AzoozAll rights reserved.Redistribution and use in source and binary forms, with or without modification, are permitted providedthat the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and thefollowing disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions andthe following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ‘‘AS IS’’ AND ANYEXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OFMERCHANTABILITYANDFITNESS FORAPARTICULARPURPOSEAREDISCLAIMED. INNOEVENTSHALL THECOPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OFSUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THISSOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.No. of lines in distributed program, including test data, etc.: 1269No. of bytes in distributed program, including test data, etc.: 179353Distribution format: tar.gzProgramming language:MATLAB 6.5 or higher.Computer: Any laptop or desktop.

✩ This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).∗ Corresponding author.

E-mail address: [email protected] (A.A. Azooz).

0010-4655/$ – see front matter© 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.cpc.2013.09.003


A.A. Azooz et al. / Computer Physics Communications 185 (2014) 350–356 351

Operating system:Windows XP.RAM: Bytes 512 KClassification: 19.Nature of problem:In RF plasma Langmuir probe diagnostics, the probe I–V characteristics obtained experimentally does notrepresent the true I–V . This is because the probe picks up some RF plasma voltage which modulates theapplied bias voltage and causes a current flow that corresponds to the RF affected bias rather that theactual DC bias. This if untreated can lead to false results for the values of plasma parameters derived fromthe obtained I–V . Several hardware based methods are used to perform such correction (compensation).Solution method:The suggested method is based on filtration of raw uncompensated I–V data through software operationrather than hardware based filtrations which have their limitations.Running time:A few milliseconds.References:[1] A.A. Azooz, Review of Scientific Instruments 79 (2008) 103501.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Since Langmuir introduced his famous method of plasmadiagnostics using the single probe, this probe is still being regardedas a powerful tool for measuring plasma properties. Interest hasgrown in using this technique over the past two decades due to theadaptation of the Langmuir probe in conjunction with computerdata acquisition systems allowing for fast, reliable, and relativelyeasy ways for obtaining and analyzing I–V probe data. Suchinformation is always necessary for any glow discharge plasmaapplication such as material deposition and surface treatment.Langmuir probe data for DC glow discharge are only affectedby the plasma electromagnetic noise which is often small andcan usually be eliminated by some straightforward methods. Thesituation is somewhat different as far as RF glowdischarge plasmasare concerned [1–3]. In spite of the fact that RF discharges arebecoming more important from an application point of view,diagnostic methods for such plasmas are still regarded as a subjectfor discussion. Langmuir probe I–V characteristics obtained for RFplasma are customarily regarded as not being truly representativeof the real I–V characteristics [4–6]. This is due to the factthat the external bias applied to the probe is not in fact theactual probe voltage which induces the current flow to the probe.Two important effects play a role in modifying the probe I–Vcharacteristics. The first is the oscillating plasma potential. Thesecond is that the probe and the system wiring picks up some RFvoltage from the plasma. Consequently, the instantaneous probecurrent is a result of these two effects rather than being dueto the DC bias alone. Unfortunately, the amplitude and phase ofthe RF voltage picked up by the probe and the plasma potentialoscillations are usually undeterminable. This results in situationswhere such probe data are considered to contain a certain degreeof ambiguity if suitable RF compensations are not applied. Severaltechniques of RF compensation have been used. These fall intothree main categories. The first is called active compensationwhere in principle, another RF voltage of a frequency equalto that of the main plasma RF is superimposed on the probeDC bias [7–9]. The amplitude and phase of this superimposedRF voltage are adjusted such that it can act to neutralize anyRF picked up by the probe from the plasma. Readjustmentsare necessary when the plasma power, probe position or probedimensions are changed. The second type of RF compensationis called passive compensation. It usually involves the use ofpassive circuit elements, usually band stop or low pass filters toprevent any RF induced current from passing through the probe

leaving only the DC probe current to be measured [10–14]. A thirdtechnique has recently gained increased interest. It is based onapplying mathematical convolution to the RF contaminated I–Vprobe characteristics to obtain the actual uncontaminated one [15].

It is the purpose here to present simulation analysis assessingthe way RF contamination affects single probe characteristics inorder to devise a simple, yet accurate method to eliminate suchcontamination.

2. Modeling and simulation

Let us assume a Langmuir probe is being subjected to an RF field.Let us further assume that the probe is biased with an arbitrary DCvoltage V . For modeling purposes, let us consider the frequencyof the RF field to be equal to 13.56 MHz which is customarilyused in plasma RF discharges. The results are identical for otherfrequencies. The overall voltage affecting the probe will be

VP = V + A1 sin(27.12 × 106π t). (1)

Let us further assume that the plasma potential is oscillatingabout themeanDC plasma potentialwith amplitude A2 at the sameRF frequency above.

In order to simulate this situation to try to obtain the trueI–V characteristics F(V ), from the RF affected characteristicsIm = g(V , A1, A2), we may use the four parameters empiricalgeneral formula for the Langmuir I–V curve proposed in Ref. [16].This equation has proven to give reasonable descriptions ofcylindrical probes’ I–V characteristics. It can also be used for otherprobes’ geometrical configurations. This equation is used here fornumerical demonstration purposes and there are no restrictionson using any other equation for that matter. The empirical I–Vrelation used is

I = exp[a1 tanh{(V + a2)/a3}] + a4 (2)

a1, a2, a3 and a4 being four free fitting parameters. Under suchcircumstance, the voltage V in Eq. (2) needs to be replaced bythe actual voltage applied to the probe which is the superpositionof the DC voltage and the RF pick up as described by Eq. (1).Furthermore, and as far as the oscillating plasma potential isconcerned, it is known that the DC plasma potential as obtainedfrom the zero crossing point of the second derivative of Eq. (2) isgiven by

Vplasma = a3 tanh−1

(1 + a21)1/2

− 1a1

− a2. (3)


352 A.A. Azooz et al. / Computer Physics Communications 185 (2014) 350–356

Fig. 1. Simulation of real time Probe I–V characteristics. (a) RF amplitude=20 V. (b) RF amplitude=40 V.

The value of the parameter a1 is only related to the ion and electronsaturation currents. These are not expected to follow any RF fieldoscillations. The same argument applies to the parameter a3 whichis themain shape determining factor in Eq. (2) and it is thus relatedto plasma electron temperature. Consequently, any RF field relatedplasma potential oscillations can be translated as oscillations in thevalue of the parameter a2 about a constant value. One can thussimulate this situation by setting

a2 ⇒ a2 + A2 sin(2π × 13.6 × 106t). (4)

The overall measured probe current affected by both plasmapotential oscillations and probe pickups can be written as

Im = exp

a1 tanh

×

V ∓ A1 sin(2π × 13.6 × 106t) + a2 ∓ A2 sin(2π × 13.6 × 106t)

a3

+ a4. (5)

Setting

A = A1 ∓ A2. (6)

Gives

Im = expa1 tanh

V ∓ A sin(2π × 13.6 × 106t) + a2

a3

+ a4. (7)

Now if we assume that the probe bias voltage V is somekind of a sweep voltage that is being recorded by some dataacquisition device as it is customary in modern Langmuir probesmeasurements to obtain the I–V characteristics, we can simulateEq. (6) to obtain Im over the entire probe bias voltage range. Resultsof such simulations are shown in Fig. 1 for two values of the RFamplitudes. The solid black line represents I–V characteristic thatshould be obtained if there were no RF effects. The values of thefour free parameters used in this simulation are a1 = 1, a2 =

−7, a3 = 7, a4 = 0.45. These parameters correspond to a plasmapotential of 10.25 V and plasma electron temperature of 4.68 eV.Other parameters values have been tested in the simulation givingsimilar results.

The scattering of data points in Fig. 1 is nothing but amanifestation of the oscillating RF voltage. It may be worthmentioning here that if the simulation sampling rate is selectedsuch that it is equal to the RF frequency divided by an integer, andusing proper triggering of the data acquisition device, will lead to

Fig. 2. Effect of several points averaging on the shape of the probe I–Vcharacteristics.

elimination of such scattering. This situation corresponds to takingsuccessive I–V data samples exactly at the moments in time whenthe RF is at zero crossing points. However, such condition is verydifficult to achieve under experimental situations.

In experimental hand measurements or those carried out withslow data acquisition devices; one only measures an average ofseveral scattered I–V data points. The number of points includedin the averaging process depends on the frequency response of themeasuring device. Fig. 2 demonstrates the effect of the numberof data points averaged on the shape of the probe I–V curveobtained as compared to a real one. It is clear that such averagingcauses large distortions. Such distorted I–V curves will certainlylead to false results regarding any deduced plasma parameters ingeneral and plasma electron temperature and the electron energydistribution function EEDF in particular.

Due to the fact that any averaging process is inherentlyassociated with loss of details, it may not be very much fruitfulto try to reconstruct the true I–V characteristics from a distortedaveraged one. Instead, it is more useful to attempt obtaining thecorrect curve using parts of the scattered data obtained frommeasurements similar to those of Fig. 1.



Fig. 3. Effect of presence of second harmonic with (a) zero phase angle, (b) π/4 phase angle.

One interesting part of the data consists of those border pointsforming the left and the right envelopes. These envelope datapoints correspond tomeasurements registered atmoments in timewhen the probe RF pickup voltage is at extreme values of +A,and –A.

For the left envelope, Eq. (5) can be written as

Iu = expa1 tanh

V + a2 + A

a3

+ a4. (8)

And for the right envelope

Il = expa1 tanh

V + a2 − A

a3

+ a4 (9)

Iu and Il corresponds to probe current values on the left andright envelopes respectively. The true probe current Ir with the RFpickup excluded is described by

Ir = expa1 tanh

V + a2

a3

+ a4. (10)

These envelope data, and as it may be evident from Fig. 1, have abehavior identical to the correct I–V curve described by Eq. (10)apart from the fact that they are shifted to the left and to the rightby A volts. Thus, isolating one of the two envelopes and correctingfor the shift will reproduce the correct I–V from these envelopedata.

In the above simulation, only the fundamental frequency com-ponent is considered. In practice however, higher RF harmonicscontaminations may also exist. These harmonics are usually oflower amplitudes. Even so, the existence of such harmonics slightlycomplicates the situation. Two types of complications arise here.The first is the fact that the right and left envelopes will be mod-ulated by the harmonic effect. The situation repeats itself if higherharmonics are considered. See Eq. (11) given in Box I.

It is clear from Eq. (11) that even when the fundamental RF is atan extreme value ∓A, the two envelopes will be modulated withamplitude B which has to be taken care of.

As far as the effect of the phase angle of second harmonic φ isconcerned, analysis has shown that the existence of such phaseangle produces some asymmetry between the second harmonicsmodulation on the two sides. This asymmetry is at maximumwhen φ = π/4. This is demonstrated in Fig. 3. However, andeven under such extreme phase related asymmetry, the amount

of phase related correction to overall shift of the I–V curve on thevoltage scale is small compared to the total voltage shift.

From the above simulation results, one can conclude that thetwo main steps necessary to reproduce the true I–V from thescattered measured real time data are:

1 — Extracting only envelope points from the bulk of the data2 — Evaluating the value of the voltage shift needed.

With present day data acquisition devices, the above two tasksare reduced to become matters of software issues.

3. The software

In the following we present a MATLAB computer code thatperforms the above two tasks. The software is freely availablefrom the program library. The software is user friendly and its usedoes not require proficiency in matlab programming apart fromsome basics. It can be used on matlab version 6.5 or higher. Thesoftware is called by entering the statement RF_compensation (V, I,Area, Mi) in matlab workspace. The input arguments are the probebias voltage (V ), and probe current (I) data arrays as acquired bythe data acquisition device. The input argument Area is the probeactive area in units of M2. Mi is the ionic mass number in amu. Asfar as the probe input voltage V and current I are concerned, it maybe worth pointing out that most common data acquisition devicesare compatible with matlab [17], or produce data files which canbe easily converted tomatlab data files. These two variables shouldbe loaded to matlab workspace prior to running the program. Thefirst task performed by the program involves separation of datapoints acquired when the sweep voltage is increasing from thoseregistered when the voltage is decreasing. This is performed bythe program separate. This is followed by sorting the pairs of datapoints in voltage ascending order using the program treat. Oncethe voltage and current raw data are organized, they are plottedas red dots. The program then starts finding the envelope pointsassociated with fundamental RF pick up. These are obtained usingthe programs maxima and minima. These two similar programslocate extreme current maxima and minima points in the data.Maxima are defined as those points with neighbor points on thetwo sides having lower values. Minimum point’s neighbors havehigher values. The maxima correspond to the first order left sideenvelope.Minima correspond to the first order right side envelope.The process is repeated twice again to handle the effect of second



Im = expa1 tanh

V + A sin(2π × 13.6 × 106t) + B sin(2π × 27.2 × 106t + φ) + a2

a3

+ a4 (11)

B and φ are the amplitude and phase difference respectively.Box I.

and third RF harmonics. Based on information from the above threefiltration processes, the amount of shift on the voltage scale neededto obtain the correct I–V is calculated. The left and right envelopesare shifted to the right and to the left by the amount calculated. Thetwo data sets are merged to form the correct I–V curve. Anotherplot containing the correct I–V is also produced. Once the data arefiltered, and the RF compensated I–V characteristics is obtained,the program calls another Langmuir probe analysis program calledAnalyze_Langmuir. This program fits the filtered data to Eq. (4).Results of fit are differentiated twice. At this stage, the plasmapotential point Vp which corresponds to the zero crossing point ofthe second derivative plot is calculated. The software now furtherproceeds to calculate and plots the electron energy distributionfunction f (E) using Druyvesteyn equation [18]

f (E) =(8m)1/2

Ane3/2(V − Vp)

1/2 d2IdV 2

. (12)

Furthermore, the software compares the deduced f (E) withMaxwell–Boltzmann and Druyvesteyn distribution laws [19]. Theplasma electron density ne is calculated by integrating Eq. (12)numerically.

ne =

∞

0f (E)dE. (13)

The plasma effective temperature Te is obtained from the electronenergy distribution function f (E).

Te =

23

∞

0 Ef (E)dE∞

0 f (E)dE. (14)

Eq. (15) uses the value of the effective temperature and theion saturation current Iis obtained from the I–V characteristics tocalculate the plasma ion density Ni [20].

Ni =Iis

Ae3/2

Mi

Te. (15)

Mi is the mass of the ion. The software converts this massfrom inputted atomic mass units to kg. It must be noted thatEq. (15) is based on the assumption of Maxwellian distributionapproximation. Thus, the values of Ni obtained my be significantlydifferent from the values of ne calculated by the software usingEq. (13). Furthermore, it may be worth pointing out that theprogram Analyze_Langmuir can be used independently to analyzeany Langmuir DCdischarge or RF filtered Langmuir probe data. Thisprogram can be freely downloaded from the matlab file exchangelibrary [21]. It can be activated by simply entering the statementAnalyze_Langmuir(V, I, Area, Mi) in the matlab workspace withinput parameters as specified above.

This software is first tested on simulated data. Results of thissimulation are shown in Fig. 4. The black solid line is the originalI–V assumed in the simulation as produced by Eq. (4) usingparameters valuesmentioned earlier. The red circles are simulateddata measurements using a sampling frequency of 8000 Hz withprobe sweep voltage amplitude of 50 Hz. The black dots are pointsof the RF corrected I–V . It is clear that this method works well inreproducing the correct I–V .

Fig. 4. Simulation results demonstrating the software ability to extract the correctLangmuir I–V curve.

Fig. 5. Experimental setup.

4. Experimentation

In order to put the above simulation results to experimentaltest, the experimental setup shown in Fig. 5 is used to producecapacitively coupled Argon plasma (CCP).

The system consists of a Teflon based bell jar glass chamber20 cm in height and 15 cm inner diameter. Two circular flat wellpolished and cleaned aluminum electrodes are installed inside thechamber. The upper electrode is 12 cm in diameter. The lowerelectrode is 5 cm in diameter. The cap between the two electrodesis 5 cm. The live RF 13.56 MHz cable from the 600 W generatoris connected to the upper electrode via an automatic impedancematching device. The Langmuir probe consists of a 0.5 mm radius,2 mm length tungsten wire connected to a 50 Hz sweep voltagesupply. The probe voltage is sampled directly from the probe via



Fig. 6. (a) Raw data acquired shown with results of three filtration processes. (b) Dots are final experimental Langmuir probe I–V . Solid line represents result of fitto Eq. (4). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Second derivative of the extracted Langmuir probe I–V at pressure of 3 Pa and RF power of 10 W. (b) The deduced EEDF compared to Maxwell–Boltzmann andDruyvesteyn distribution laws.

a potential divider (not shown in Fig. 5) to reduce the maximumvoltage signal to less than one volt which is the maximum inputrating for the computer sound card used as the 8000 data samplesper second data acquisition device. The probe current sampling iscarried out across the series 1 K� resistance. It is worth noting thatall cable connections used are of the earthed coaxial type. ManyLangmuir probe I–V characteristics measurements at differentRF powers and Argon gas pressures are carried out. Detailedanalysis of results will be presented elsewhere. However, and fordemonstration purpose, results at 10W, and 3 Pa RF power and gaspressure respectively are analyzed using the procedure describedabove

5. Results and discussion

The experimental raw data as acquired by the computer areshown as red dots in Fig. 6. The data show scattering of pointsover a wide region. Data at other RF power values show similarbehavior. These data are subjected to three filtration processesto remove the first, second, and third harmonics. The resultsof the first filtration are indicated as diamonds surrounding theunfiltered data on the same figure. Data points resulting from thesecond filtration are shown as circles surrounding the diamondmarkers. The results of the third filtration are plotted as blacksolid lines. These represent the ultimate two envelopes enclosing



Table 1Comparison between plasma parameters obtained using filtered and unfiltered Langmuir probe data.

Plasma parameter Plasma electrontemperature Te (eV)

Plasma potential(V)

Flouting potential(V)

Ion density Ni1015(M−3)

Electron density Ne1016(M−3)

Uncompensated data 9.12 11.01 −5.42 5.5 1.32Compensated data 7.44 8.62 −4.28 5.6 1.51

Fig. 8. Comparison between energy distribution functions obtained using filteredand unfiltered Langmuir probe data.

the raw data. The two envelopes obtained are shifted by theappropriate amount on the voltage scale to the middle pointbetween them and their data are combined to obtain the actualLangmuir probe I–V . The results of such a shift are presented asdots in Fig. 6(b). These data are fitted to Eq. (4). The fitted curveis differentiated twice. The result of such a differentiation areplotted in Fig. 7(a). The plasma static potential is obtained from thezero crossing point of the second derivative. The second derivativeis further used to obtain the electron distribution function(EEDF) using Druyvesteyn equation [19]. The EEDF is shown inFig. 7(b).

In order to demonstrate the effectiveness of this RF compensa-tion technique, the uncompensated data are also analyzed to ob-tain the plasma parameters. The results of both types of analysisare presented in Table 1. It is clear that the applied compensationtechnique gives significantly lower values for both plasma electrontemperature and plasma potential. Fig. 8 shows the electron en-ergy distribution function derived from compensated and uncom-pensated data. It is clear that the applied compensation succeeds

in reducing the high energy tail and shifting the most probable en-ergy value to the left. This is consistent with results expected fromapplying any compensation procedure.

6. Conclusion

Anewmethod for treatment of the problemof RF compensationin Langmuir probe plasma diagnostics is suggested and tested. Themethod replaces active or passive compensation procedures usingexperimental hardware systems by a simple, yet effective softwaretreatment of uncompensated experimental data. Special matlabbased software is written to perform this task. The software canbe downloaded from the program library.

References

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Supplement.[16] A.A. Azooz, Rev. Sci. Instrum. 79 (2008) 103501.[17] http://www.mathworks.com/pl_daq.[18] M. Druyvesteyn, F. Penning, The mechanism of electrical discharges in gases

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probe-data-analysis-code.

langmuir double probe rf plasma compensation using simulation method

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