A calorimetric probe for plasma diagnosticsMarc Stahl, Thomas Trottenberg, and Holger Kersten Citation: Review of Scientific Instruments 81, 023504 (2010); doi: 10.1063/1.3276707 View online: http://dx.doi.org/10.1063/1.3276707 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/81/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Response to “Comment on ‘Water bath calorimetric study of excess heat generation in resonant transferplasmas’ [J. Appl. Phys.96, 3095 (2004)]” J. Appl. Phys. 98, 066109 (2005); 10.1063/1.2010617 Comment on “Water bath calorimetric study of excess heat generation in resonant transfer plasmas” [J. Appl.Phys.96, 3095 (2004)] J. Appl. Phys. 98, 066108 (2005); 10.1063/1.2010616 LabView virtual instrument for automatic plasma diagnostic Rev. Sci. Instrum. 75, 90 (2004); 10.1063/1.1634356 Plasma diagnostics for the sustained spheromak physics experiment Rev. Sci. Instrum. 72, 556 (2001); 10.1063/1.1318246 Diagnostics of the diamond depositing inductively coupled plasma by electrostatic probes and optical emissionspectroscopy J. Vac. Sci. Technol. A 17, 138 (1999); 10.1116/1.581563

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A calorimetric probe for plasma diagnosticsMarc Stahl, Thomas Trottenberg, and Holger Kerstena�

Institute of Experimental and Applied Physics, Christian-Albrechts-University Kiel, D-24098 Kiel, Germany

�Received 14 October 2009; accepted 29 November 2009; published online 19 February 2010�

A calorimetric probe for plasma diagnostics is presented, which allows measurements of the powertaken by a test substrate. The substrate can be biased and used as an electric probe in order to obtaininformation about the composition of the total heating power. A new calibration technique forcalorimetric probes, which uses monoenergetic electrons at low pressure, has been developed for animproved accuracy. The use of the probe is exemplified with an experiment where both energeticneutral atoms and ions heat the test substrate. © 2010 American Institute of Physics.�doi:10.1063/1.3276707�

I. INTRODUCTION

Plasma-wall interactions are very important in a widevariety of plasma applications, in particular for etching andthin film deposition. For such treatments the thermal andenergetic conditions at the substrate surface are crucial. Thesubstrate temperature is considered to be the primary controlparameter for deposition of thin films because the involvedatomic processes, such as adsorption, sputtering, implanta-tion, diffusion, and chemical reactions, are all temperaturedependent.1,2 The energy flux, i.e. the product of incidentparticle energy and particle flux, is not only the cause ofsubstrate heating, but is also known to determine surface filmetching and sputtering rates in plasma and ion beam etchingapplications.3,4

Therefore, the energy flux to the substrate �power perarea� is a key parameter in such plasma processes.5 In gen-eral, the total power input Pin to a substrate can be describedby

Pin = Pi + Pe + Pn + Prad + Pfilm, �1�

where Pi, Pe, and Pn are the kinetic contributions of the ions,electrons, and neutral atoms, Prad is the radiation from hotsurfaces or the plasma itself, and Pfilm is the released powerduring film growth due to condensation, adsorption, andchemical reactions. The single contributions are described indetail in Ref. 6. In order to estimate the transferred power,several techniques have been developed7–12 and relatedmeasurements have been performed in many processplasmas.13–15 A simple measurement technique based on tem-perature measurements known as the calorimetric or thermalprobe has been introduced by Thornton.16

The article is organized as follows. Section II is a shortsummary of the calorimetric method followed by a descrip-tion of the probe design in Sec. III. Section IV is dedicated toa new calibration technique. Finally we show an example ofuse.

II. CALORIMETRIC METHOD

The principle for measuring the incoming power is basedon the rate of change in the temperature of a test substrate,dTS /dt, which implies measuring the temperature character-istic of the heating process when the probe is exposed to anenergy flux and the following cooling without this energyflux �Fig. 1�. The change in the heat content �enthalpy HS� ofthe test substrate can be described by

dHS

dt= CS ·

dTS

dt, �2�

where CS is the effective heat capacity of the substrate in-cluding the connected wires and the interaction with theholder. The balance of power during the heating process isgiven by

dHS,h

dt= Pin − Pout�TS� , �3�

and during the cooling process by

dHS,c

dt= − Pout�TS� . �4�

If the incoming power Pin is constant during the heatingprocess and the heat loss Pout�TS� is only a function of thesubstrate temperature, the incoming power can be calculatedby subtracting Eq. �4� from Eq. �3� for each temperature TS

measured during the heating �TS,h=TS� and the followingcooling processes �TS,c=TS�:

Pin�TS� = CS · �dTS,h

dt−

dTS,c

dt�

TS

= CS · F�TS� . �5�

The function F�TS� is used as an abbreviation for the differ-ence of the temperature slopes, and is defined for all sub-strate temperatures TS adopted during both the heating andthe cooling phases. Since the procedure yields a set of valuesPin�TS� corresponding to the set of temperatures TS, there aredifferent ways to determine a representative value.

The technique applied in this work is as follows. Theenergy flux is calculated from the average �Pin�TS��, and the

a�Electronic mail: kersten@physik.uni-kiel.de. URL: http://www.ieap.uni-kiel.de/plasma/ag-kersten/.

REVIEW OF SCIENTIFIC INSTRUMENTS 81, 023504 �2010�

0034-6748/2010/81�2�/023504/4/$30.00 © 2010 American Institute of Physics81, 023504-1

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standard deviation of all Pin�TS� is taken as its error. Thiserror already accounts for a possible nonlinearity of dHS /dtin TS �see Eq. �2��, i.e., a drifting CS.

An alternative procedure assumes that the releasedpower Pout�TS� is linear in TS, and is a good approximationwhen heat conduction to the background gas and the ceramicholder at constant temperatures is the dominating coolingmechanism. Heat radiation and convection, which becomeimportant at high substrate temperatures and gas pressures,respectively, introduce nonlinear terms in Pout�TS�. Underthe assumption of linearity, the raising and falling parts ofthe temperature characteristic �see Fig. 1� are exponentialcurves. The exponential fits yield a unique value Pin

= Pin�TS� for all TS.A third method evaluates the temperature characteristic

only for small deviations from the equilibrium temperature,so that Pout�TS� vanishes.17 The temperature slope at the be-ginning of the heating phase dTS,h /dt, which is preferablyshort, is measured and the falling temperature slope is ne-glected �dTS,c /dt=0�. The simplified Eq. �5� yields a uniquevalue for Pin. This technique is not affected by a drifting CS

and a nonlinearity of Pout�TS�. However, the condition of asmall deviation from the equilibrium temperature can oftennot be accomplished because of too high energy fluxes orunstable plasmas immediately after starting the discharge.

For all three methods the exact knowledge of the effec-tive heat capacity of the calorimetric probe CS is essential forthe calculation of the incoming power Pin.

III. PROBE DESIGN

The calorimetric probe is shown in Fig. 2. As test sub-strate either a 0.1 mm copper or a 0.05 mm tungsten circularfoils with a diameter of 20 mm is used. The thermocouple�type K� for the temperature measurement and an additional

copper wire for biasing �US� and current measurements�IS� are brazed to the back of the substrate. The substrateis placed into a ceramic shield �Macor™� for thermal insu-lation. Furthermore, it has a much higher heat capacity�Ccer=18 J /K� than both substrates �CCu=0.11 J /K, CW

=0.04 J /K�, which ensures low variation of the ceramictemperature. The probe is mounted on a rotatable andmovable metal rod for spatially resolved measurements atdifferent tilt angles. The measured temperature signal�40.44 �V / °C� is amplified in the vacuum chamber nearthe feedthrough by a thermocouple amplifier AD 595 withcold junction compensation and built-in ice point reference.The amplified signal is passed through a low-pass filter of340 Hz and recorded at a sample rate of 20 Hz using a 13-bitanalog-digital converter.

IV. CALIBRATION OF THE PROBE

Taking into account just the heat capacity of the meresubstrate instead of the effective heat capacity of the probe isvalid only for large substrates. However, large probe sub-strates would lead to a very long measurement time. Ourprobe has been developed for short measurement times andspatially resolved measurements and therefore requires smallsubstrates. Because of the wiring and the contact to theholder the effective heat capacity of the calorimetric probecannot be calculated. Thus, the effective heat capacity has tobe measured by applying a known power to the substratesurface �see Eq. �5��, and the validity of Eqs. �2� and �5� hasto be shown. In former experiments a laser has been used,18

but difficulties in the estimation of the reflectivity of thesubstrate result in dissatisfying errors of the measurements.19

Another calibration technique was developed by Wendtet al.,20 where electrons from a plasma were used as an ad-justable power source depending on the substrate bias. Theenergy flux measurement was performed in combinationwith Langmuir probe measurements. However, extractingelectrons from the plasma can change the plasma itself sig-nificantly. Hence, the other power contributions in Eq. �1� arenot necessarily constant.

To overcome these difficulties we applied for the firsttime a very simple setup for the calibration, which uses a hotfilament as electron source �Fig. 3�. The probe is placed in avacuum chamber at about 10−4 Pa to ensure a sufficientmean free path of the electrons. The 100 �m tungsten wireis heated by a current of about 1.5 A at a voltage of UH

=10 V and is additionally negatively biased �UW=−80 V�to push the emitted electrons away. The calorimetric probeplaced at a distance of 10 cm is positively biased �US� to

FIG. 1. �Color online� Temperature characteristics TS�t� of the calorimetricprobe displaying heating and cooling curves. The power was supplied by anelectron beam at different voltages.

FIG. 2. �Color online� Sketch of the calorimetric probe.

FIG. 3. �Color online� Schematic of the experimental setup for the calibra-tion of the calorimetric probe by electrons as a known power source.

023504-2 Stahl, Trottenberg, and Kersten Rev. Sci. Instrum. 81, 023504 �2010�

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accelerate the incident electrons to a defined kinetic energyfor substrate heating by dissipation of the kinetic electronenergy. The current-voltage characteristic is similar to a di-ode tube. The resulting electron power Pe for heating isgiven by

Pe = US − UW +UH

2 · IS, �6�

where IS is the measured electron current through the calori-metric probe. The term UH /2 accounts for the mean voltagedrop along the filament. During the cooling phase it is nega-tively biased to prevent the electrons from reaching the sur-face �IS=0�.

The substrate �probe� is also exposed to the heat radia-tion of the emitting tungsten wire. However, this contributionis always present and constant. Thus, only the electrons arecontributing to the measured incoming power Pin= Pe.

Figure 4 shows the calibration data for a copper and atungsten probe. The electron power Pe is plotted against themean value of F�TS�. The data can be well described by astraight line through the origin. This indicates that the heat-ing and the cooling of the probe obey Eqs. �2� and �5� withan effective heat capacity of the probe, which corresponds tothe slope �see Eq. �5��. The resulting effective heat capacitiesof the different calorimetric probes are CS,Cu=283 mJ /K forcopper and CS,W=181 mJ /K for tungsten, which are muchhigher than the heat capacities of the substrates themselves.The single measurement does not deviate more than 3% fromthe best fit, hence, we give this upper limit as the error of CS.This accuracy enables reliable conclusions about the totalincoming power in process plasmas.

V. EXAMPLE OF USE FOR THE CALORIMETRICPROBE

In the following the use of the calorimetric probe is il-lustrated by measurements in a well-understood ion broadbeam experiment.21 The energy flux is dominated by ener-getic argon ions and neutral argon atoms. The energetic at-oms stem from charge-exchange collisions that discharged apart of the beam ions. There are no other relevant energy

sources heating the probe substrate, which keeps the experi-mental situation simple and makes it well suited for a dem-onstration of the thermal probe.

The energy of the ions is set by means of the anodevoltages UA=200,300,400 V in the ion source. The plasmapotential was measured with a Langmuir probe and is some60 V above the anode potential, i.e., Upl�UA+60 V. A two-grid system with a diameter of 125 mm is used to extract andaccelerate the ions. The argon pressure in the chamber was5�10−2 Pa, which provides a short mean free path forcharge-exchange collisions of �cx= �25�3� cm. This means,that at a distance of z=30 cm from the ion source onlyexp�−z /�cx�= �30�5�% of the argon beam is still ionizedand the other 70�5% of the beam consist of energetic neu-tral argon atoms.

The probe is biased with US=−20 V to prevent plasmaelectrons from the target chamber from reaching its surface.However, there still might be an error due to secondary elec-trons produced by the impinging ions at the probe surface.Such secondary electrons lead to measured currents higherthan the ion current itself. Depending on the condition of thesurface and the ion energy, this error could be up to 10% ofthe ion current.22

Figure 5 shows the measured energy fluxes and currentsat the distance z=30 cm for different radial positions in thebeam. The errors for the higher incoming powers of approxi-mately Pin=1 W are significantly higher than for the smallerenergy fluxes. This can be explained with the heating of theceramic holder which alters the effective heat capacity CS

during the measurement and leads to a broadening of thefunction F�TS�. In such cases the temperature characteristics

FIG. 4. �Color online� Calculated electron beam power Pe against the meanvalue of the distribution F�TS� calculated from the corresponding tempera-ture characteristics. The effective heat capacities are obtained from theslopes.

FIG. 5. �Color online� Radially resolved measurements of �a� incomingpower Pin and �b� current IS in a distance of 30 cm to the grid system of theion beam source for three different anode voltages UA=200,300,400 V.

023504-3 Stahl, Trottenberg, and Kersten Rev. Sci. Instrum. 81, 023504 �2010�

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of the probe should be analyzed with the third method listedin Sec. II, which is based on the slope at the equilibriumtemperature.

One can estimate the contribution of the ions Pi to thetotal energy flux Pin from the measured ion current and thekinetic ion energy gained in the potential drop Upl−US fromthe source plasma down to the probe surface:

Pi = �Upl − US� · IS. �7�

The calculated ion powers for the center of thebeam are derived from the corresponding currents IS

=0.18,0.33,0.59 mA are Pi=50,125,283 mW for thethree anode voltages UA=200,300,400 V, respectively. Wecompare this to the measured beam powers Pin

=190,450,1000 mW. The ratio Pi / Pin�0.3 is in goodagreement with the expectation based on the composition ofthe beam �30% ions and 70% neutral atoms�.

VI. CONCLUSION

In this work a calorimetric probe for the diagnostic ofindustrial plasma applications and laboratory plasma experi-ments was presented. A simple theory known from previousexperiments for the interpretation of the measured tempera-ture characteristics was summarized and the validity andlimitations of the model were discussed. A novel calibrationtechnique using energetic electrons has been developed. Asan example for the application of the probe, measurements inan ion beam experiment were performed. The composition ofthe beam, which consists of energetic ions and neutral atoms,could be confirmed by a simultaneous measurement of theion current onto the probe substrate.

ACKNOWLEDGMENTS

The technical assistance of Michael Poser and VolkerRohwer as well as the experimental assistance of VictorSchneider and Pierre-Antoine Cormier is gratefully acknowl-edged.

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023504-4 Stahl, Trottenberg, and Kersten Rev. Sci. Instrum. 81, 023504 �2010�

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