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Breakdown study of dc silicon micro-discharge devices

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2012 J. Phys. D: Appl. Phys. 45 065201

(http://iopscience.iop.org/0022-3727/45/6/065201)

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 45 (2012) 065201 (11pp) doi:10.1088/0022-3727/45/6/065201

Breakdown study of dc siliconmicro-discharge devicesL Schwaederle1, M K Kulsreshath1, L J Overzet2, P Lefaucheux1,T Tillocher1 and R Dussart1

1 GREMI, CNRS/University of Orleans, 14 rue d’Issoudun, BP 6744, 45067 Orleans Cedex 2, France2 PSAL, University of Texas at Dallas, 800 W. Campbell road, RL10, Richardson, TX 75080-3021, USA

E-mail: laurent.Schwaederle@univ-orleans.fr

Received 28 October 2011, in final form 4 January 2012Published 30 January 2012Online at stacks.iop.org/JPhysD/45/065201

AbstractThe influence of geometrical and operating parameters on the electrical characteristics of dcmicrocavity discharges provides insight into their controlling physics. We present here resultsof such a study on silicon-based microcavity discharge devices carried out in helium atpressure ranging from 100 to 1000 Torr. Different micro-reactor configurations weremeasured. The differences include isolated single cavities versus arrays of closely spacedcavities, various cavity geometries (un-etched as well as isotropically and anisotropicallyetched), various dimensions (100 or 150 µm cavity diameter and 0–150 µm depth). Theelectrode gap was kept constant in all cases at approximately 6 µm. The applied electric fieldreaches 5 × 107 V m−1 which results in current and power densities up to 2 A cm−2 and200 kW cm−3, respectively. The number of microcavities and the microcavity depth are shownto be the most important geometrical parameters for predicting breakdown and operation ofmicrocavity devices. The probability of initiatory electron generation which is volumedependent and the electric field strength which is depth dependent are, respectively, consideredto be responsible. The cavity shape (isotropic/anisotropic) and diameter had no significantinfluence. The number of micro-discharges that could be ignited depends on the rate of voltagerise and pressure. Larger numbers ignite at lower frequency and pressure. In addition, thevoltage polarity has the largest influence on the electrical characteristics of themicro-discharge of all parameters, which is due to both the asymmetric role of electrodes aselectron emitter and the non-uniformity of the electric field resulting in different ionizationefficiencies. The qualitative shape of all breakdown voltage versus pressure curves can beexplained in terms of the distance over which the discharge breakdown effectively occurs aslong as one understand that this distance can depend on pressure.

(Some figures may appear in colour only in the online journal)

1. Introduction

For ‘unique features resulting from their ability to sustainlarge current densities and power depositions on a continuousbasis’ [1] and evident reasons of lower cost and simplifiedoperation in comparison with their low-pressure counterparts,high-pressure (about atmospheric pressure) plasma processesare of great interest [2]. In many technological applications, anon-thermal plasma operating in the glow mode is required[3, 4]. However, maintaining such a stable diffuse glowdischarge plasma at high pressure is challenging due to their

susceptibility to transition to an arc [5]. One way to stabilizesuch a high-pressure plasma is to spatially confine it todimensions below about 1 mm, leading to the so-called worldof microplasmas. The stable operation of a microplasma canbe explained through the pd similarity law, where p and d

represent, respectively, the pressure and the discharge gap(which corresponds to the electrode separation if care is takento prevent ‘long-path breakdown’). This Paschen law [6] statesthat the breakdown voltage depends on pd product instead ofdepending individually on p and d. At low pressure, stableoperation of glow discharges is possible for pd in the range of

0022-3727/12/065201+11$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

about 1–10 Torr cm where the breakdown voltage is minimum.In this way, for stable operation at high pressure, one onlyneeds to decrease the discharge gap while keeping the pd valuein the same range to allow ignition at low voltages. Indeed,discharge operation is unstable at high pressure while keepingthe same d as in the low-pressure case, which correspondsto pd values higher than 10 Torr cm. It is due to the highcurrent density, particularly in the cathode sheath, which is asource of instability and may lead to the glow-to-arc transition(GAT). Also, the dominance of boundary phenomena in suchmicroplasmas, with small volume-to-surface ratio comparedwith low-pressure plasmas probably plays a stabilizing role.However, in spite of pd similarity of the microplasma and itslow-pressure counterpart, the current densities in the formerone are much higher, making microplasmas not simply a scaleddown version of a low-pressure plasma.

Many different microplasma types exist depending on thedevice structure and operating mode. Several reviews havealready been published on that topic [7–9]. The present studieddevices are of ‘MHCD’ (micro hollow cathode discharge) type.That acronym historically refers to a specific mode of dischargeoperation, the ‘hollow cathode’ mode in which the dischargehas a negative differential resistance. The first ‘MHCD’ wasobtained by scaling the well-known hollow cathode dischargeto a submillimetre size [10] before it was shown [11] thatthe hollow cathode effect was not effective in the MHCD.Thus, that nomenclature might be misleading because thatkind of micro-discharge is generally operated in the normalor abnormal glow mode. Some authors encourage insteadthe adoption of names such as ‘microplasma’, ‘microcavityplasma’ or ‘microdischarge’.

Despite their interesting properties—stability, high-pressure operation, non-equilibrium, high power density—their small size could drastically limit their range ofapplications. However, it is possible to enlarge the plasmavolume either by arranging such micro-discharges in arrays,by extending it when used as a plasma cathode with a thirdelectrode positively biased and located some distance away[12] or using both techniques [13]. One method used to ignitearrays of micro-discharges is to limit the current driven byeach micro-discharge through the use of either individual [14]or distributed [15] ballast resistors. Another way, without useof any ballast, is to ‘force’ the micro-discharge to operate underconditions where the slope of the V –I characteristic is positive,that is in an abnormal regime. This is possible by limiting thecathode surface area [10, 16, 17].

The first reported micro-discharge device fabricated insilicon consists in a single closed cavity 200–400 µm indiameter and 0.55 mm in depth [18]. Operated in dc andusing the silicon substrate as the cathode, thus limiting thecathode area because of the finite cavity depth, it showed astable operation in Ne and N2 from a few hundred Torr upto atmospheric pressure. Moreover the V –I characteristicexhibited a positive differential resistance over the entirecurrent and pressure range. It opened the way to operation ofsilicon-based micro-discharge arrays. Shi et al [15] succeededin igniting Si-integrated micro-discharge arrays (4 × 4) in dc,without limiting the cathode area, using silicon (resistivity

of 1200 � cm) for anode material as a distributed resistiveballast. Many other studies have been carried out on silicon-based microplasma reactors, e.g. [19–21]. No systematic studyof the influence of geometrical and operating parameters onbreakdown and operation of microcavity discharges has beendone yet. Chen et al [20] studied the operation of three differentcavity shapes made within silicon with the same cross-sectionalopening area. The conclusions concerning the influence ofgeometrical and operating parameters on the operation of thedischarge are the following. Whatever the microcavity shape(planar, inverted pyramid or vertical cavity), experiments showthat the higher the cathode surface the higher the current drivenby the microcavity discharge for a given voltage. It is about oneorder of magnitude higher for the deepest cavity compared withthe non-etched one. The operation of the non-etched cavitieshas been shown to be more sensitive to pressure comparedwith both etched ones, requiring more voltage to drive a givencurrent as the pressure decreases. In the case of arrays, with thesame microcavity shapes, the higher the number of cavities, thehigher the total current driven for a given voltage. Concerningbreakdown voltage, it has only been mentioned that in the caseof arrays it does not vary significantly with the array size.

In our lab, we make use of conventional semiconductormicro-fabrication technologies to design microcavity reactorsintegrated in silicon substrate and take advantage of theintrinsically limited cathode area of the etched cavities to ignitearrays of micro-discharges [22]. The features of the presentstudied microdevices are the use of silicon as the micro-reactorcathode, the limitation of the cathode area (due to the closedcavity), the opening diameters from 150 to 25 µm and the useof a very thin dielectric thickness (∼6 µm) inducing an appliedelectric field as high as 5 × 107 V m−1.

This study has been undertaken to better understand theinfluence of geometrical and operating parameters on thebreakdown and operation of such microcavity discharges.

2. Experimental set-up

2.1. Micro-reactors

As an example, the upper portion of figure 1 shows the frontview of a micro-reactor consisting in a 1024 microcavitiesarray with opening diameter D = 100 µm. The chip is about1.5 × 1.5 cm2. It consists of an electrode/dielectric/electrodesandwich structure containing cavities. Silicon substrate(n-type, resistivity of 5000 � cm) is used as one electrodeand nickel as the other. SiO2 is used as the dielectric. Thethicknesses of layers are about 6, 6 and 500 µm for the nickel,the SiO2 and the silicon, respectively. Figure 1 (upper part)shows three different square zones. The inner and intermediateones are both the nickel layer and the third one is the siliconoxide layer. Both the intermediate one and the outer one arecovered with photoresist to prevent edge breakdown. Thefabrication process used has already been detailed [22, 23].Several micro-reactor configurations are realized as singlecavity, 16 × 16 = 256 and 32 × 32 = 1024 cavities arrayswith different opening diameter and a few others which havenot been used in this study. The cavity opening diameter is

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 1. (top) Front view of a 1024 microcavities array withD = 100 µm; (bottom) cross-sectional view of the structure of bothtypes of cavity.

ranging from 25 to 150 µm. For array configurations, thedistance between cavities, from edge to edge, is the sameas the corresponding cavity diameter. The cavity shape canbe isotropic or anisotropic (figure 1 (bottom)) depending onthe etching process used [22]. Using the anisotropic process,it is possible to etch cavities to a depth of a few hundredmicrometres or even through the silicon substrate. The volumeof such a cavity is of the order of a few 10−3 mm3.

2.2. Electrical circuit and experimental procedure

The experiments are carried out in a ∼2 litre stainless-steelcylindrical chamber. It is equipped with a pumping system(diaphragm and molecular pumps) allowing the chamber tobe evacuated to a few 10−6 mbar. A gas input system allowsexperiments in different gases or mixture of gases (proportionscontrolled by partial pressure). Pressures could be set from afew tens to 1000 Torr. It is also equipped with an electricalinput for the connection with the power supply/measurementcircuit, a few windows for the operating control of the dischargeand optical diagnostic and a micro-reactor positioning system.In this study, experiments are performed with helium withinthe pressure range 100–1000 Torr. A Baratron gauge and aPirani gauge are used for measurement of working and basepressures respectively.

The micro-reactors are powered using a dc powersupply. The electrical set-up is complemented withequipment for measurement of electrical parameters. The

Figure 2. Powering and measurement circuit.

powering/measurement electrical circuit is shown in figure 2.The powering part includes a 1500 V/150 mA dc power supplyunit and a ballast resistor Rb to limit the current. Forthe present experiments Rb = 39 k�. The power unitcan be controlled manually or using an external functiongenerator. The function generator was used to generate atriangular voltage signal for acquiring the V –I characteristicsand for breakdown voltage measurements. To obtain theV –I characteristics for both increasing and decreasing current,the discharge voltage and current are acquired during oneperiod of the triangle wave. For the determination of thebreakdown voltage, the acquisition of discharge voltage andcurrent during eight periods was made in order to obtain anaverage value, for each pressure. The signal frequency used forV –I characteristic acquisition f is either 50 mHz or 200 mHzdepending on the study. For breakdown voltage determination,f = 200 mHz in all cases which corresponds to a voltagerate of about 200 V s−1. The measurement part of the circuitincludes a resistance in series with the micro-reactor for itscurrent measurement Rm = 1 k�, a digital oscilloscope andhigh voltage probes for voltage measurements. The anodeVA and cathode VC voltages are recorded. The dischargevoltage Ud = VA − VC and current Id = VC/Rm are deducedfrom those measurements. On the breakdown voltage versuspressure curve Vbr = f (P ), each plotted point representsthe average of eight voltage values. The error bars, shownon all graphs, are considered as random errors and obtainedconsidering Gaussian distribution of experimental values andtaking the width of the approximated distribution profile. Thatuncertainty in measurement is calculated individually for eachpressure to check for a possible dependence of the distributionwidth on pressure.

3. Results

3.1. Geometrical parameters

3.1.1. Cavity shape. To investigate the influence of thecavity shape on the operation of micro-reactors, we havetested two micro-reactors with the same configuration, thatis arrays of 32 × 32 = 1024 cavities with opening diameterD = 100 µm, but with different cavity shapes. One isanistropically etched and the other isotropically etched asshown in figure 3 after operation. Note that the completemicro-reactor structure (electrode set separated with dielectric)is not visible in the pictures because the nickel electrode

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 3. SEM cross-section views of anisotropic (a) and isotropic(b) D = 100 µm opening diameter cavity after operation.

has been removed during the cleavage of the micro-reactors.The upper layer corresponds to the dielectric (SiO2) andthe lower one, holding the cavity is the Si electrode. Thegeometrical features of cavities of both types of micro-reactorsare indicated in table 1. For calculation of each cavity cathodesurface area and cavity volume, they are considered either ascylindrical (anisotropic cavity) with diameter Dcav = D =100 µm and depth l = 150 µm or as hemispheric (isotropiccavity) with diameter Dcav = 130 µm (due to a symmetricalundercut of about 15 µm). The cathodic surface and volumeof the isotropic cavity are both half the anisotropic ones.Breakdown voltage measurements have been done in heliumat a pressure ranging from 50 to 1000 Torr. The electrodesseparation (dielectric thickness) is about 6 µm for all themicro-reactors tested in this study which corresponds to arange of the pd product, for the anisotropic case of 0.03–0.6 Torr cm. Actually, these values are given as an indicationbut are not well defined because of the non-uniformity ofthe electric field. For that reason and the non-similarity ofelectric field of the different studied cases, the breakdownvoltage curves are presented with respect to pressure. In the

isotropic case, due to an undercut of about 15 µm and if weconsider the electrode gap as the shortest distance betweenelectrodes, i.e. d ∼ 20 µm, the corresponding pd range is0.2–2 Torr cm. With respect to the well-known Paschen’scurve for breakdown voltage, in the case of parallel planeelectrodes, in helium gas, we are located, in both cases inthe region of the left branch ((pd)He

min � 5 Torr cm). Figure 4shows the averaged breakdown voltages Vbr versus pressureP for both types of micro-reactors. We can immediatelynote that, although the cavity shapes are very different, thecorresponding breakdown curves versus pressure are verysimilar and match quite well, with a small tendency for highervalues for the isotropic case. Generally speaking, during eachvoltage period, a few micro-discharges ignite one after theother and operate together at the highest driven current, whichranges between a few mA to 20 mA maximum (in order tonot damage the micro-reactors). Their number varies fromone to five and remains very small with respect to the totalnumber in the arrays (1024). For determination of breakdownvoltage curves, only the first breakdown voltage values of eachramp have been used. Figures 5 and 6 show the dischargevoltage and current versus time and the corresponding V –I

curves, obtained in He at P = 500 Torr for anisotropicand isotropic cavity micro-reactors respectively during oneperiod of powering voltage signal. There are similarities inboth cases. First, after breakdown has occurred, the micro-discharge enters in an abnormal glow regime, with a linearincrease in discharge voltage with current. The immediateentrance in abnormal regime (which is one of the necessaryconditions for operation of micro-discharge array [17]) is dueto the intrinsic limited coverage of the cathode surface insidethe microcavity. The extension of the cathode sheath areabeing limited by the cavity surface, the discharge current Id

can only increase if the externally applied voltage increases.Second, the abnormal regime allows successive ignition of afew micro-discharges in both cases. We can notice that, even ifthe number of ignited discharges remains small in both cases,the tendency in the isotropic case is to ignite more micro-discharges (generally, two times more: 4 compared with 2). Onthe other hand, the voltage drop after the successive ignitionsis in general lower in the isotropic case, which is characterizedby an abnormal regime whose differential resistance is slightlyhigher (r ∼ 25 k�) compared with the anisotropic cavity(r ∼ 17 k�). That difference in differential resistancemight be due to the smaller cathode surface in the case ofisotropic cavities (steeper abnormal regime in that case). Thiscan explain the slightly higher number of micro-dischargesignited in the isotropic case because it is faster in that caseto reach again the breakdown voltage. The voltage dropafter breakdown, i.e. the gap between breakdown voltage andthe sustaining voltage immediately after breakdown, togetherwith the differential resistance of the abnormal regime arekey parameters for ignition of micro-discharges in parallel.But those differences do not seem to come as much fromthe cavity shape (anisotropic/isotropic) as from the availablesurface area of the cathode surface. Indeed, as indicated intable 1, the cathode surface in the isotropic case is half ofthat in the anisotropic case and Dufour et al [17] have shown

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Table 1. Geometrical features of the cavities (shown in figure 3) of the micro-reactors (32 × 32 = 1024 with D = 100 µm) used for cavityshape study; D: opening diameter, dn: distance to the nearest neighbour cavity, Dcav: inner diameter, l: depth, Scath: wall surface (cathodesurface), V : volume.

D (µm) dn (µm) Cavity type Dcav (µm) l (µm) Scath (mm2) V (mm3)

100 100 Anisotropic 100 150 0.055 1.18 × 10−3

100 100 Isotropic 130 75 0.027 0.58 × 10−3

Figure 4. Breakdown voltage Vbr versus pressure P for the twomicro-reactors (1024 array with D = 100 µm) with different cavityshapes: anisotropic and isotropic.

that the smaller the cathodic surface, the more emphasized theabnormal glow regime. Concerning the ignition of microcavitydischarges in array configuration, it is worthwhile to say that wecould probably control the number of ignited micro-dischargeswith variation of the slope and amplitude of the voltage ramp.

3.1.2. Micro-reactor configuration. The influence of themicro-reactor configuration on both breakdown and operationof micro-discharges has been studied using three micro-reactors consisting of identical cavities but with differentconfigurations: 1024 cavities array, 256 cavities array andsingle cavity. The cavities are identical in shape (anisotropic)and dimensions (diameter D = 100 µm, depth l = 150 µm).The breakdown voltage curves versus pressure obtained inhelium for pressure ranging from 100 to 1000 Torr are shownin figure 7(a). Qualitatively the three curves have the sameshape and also the same shape as those obtained in the studyof the cavity shape. Nevertheless, the values of breakdownvoltage for the single-cavity configuration is about 100 Vhigher than that for the two array configurations over the fullpressure range. Two hypotheses may be given to explainthis observation. The first one originates from the fact thatgaseous electrical breakdown is a stochastic process. That isto say: its actual occurrence depends on the probability thatan initiatory/seed electron will be available and that it willlead to an avalanche of sufficient size for the development ofa conductive breakdown channel in the gas. That initiatoryelectron must be available in a suitable location (preferablyclose to the cathode) for maximum electron amplification. Aswe already stated, the measurement of the breakdown voltage iscarried out by powering the micro-reactor using an increasingvoltage ramp. The rise time is 2.5 s. During this period, the

Figure 5. Discharge voltage and current versus time for the 1024,D = 100 µm cavities array micro-reactor, in both anisotropic (a)and isotropic (b) cases, during a period of the voltage power supply(f = 200 mHz, T = 5 s), in He at P = 500 Torr.

discharge can only be ignited if the electron density reaches acritical value. The real time needed to reach that critical valueafter the voltage has reached the minimum static breakdownvoltage, Vs, that is the lowest breakdown voltage which wouldignite the discharge after a sufficiently long application time,is the breakdown delay time [24]. It is statistically distributedand consists of two parts t = ts + tf : the statistical time ts whichis the time that elapses from the moment when Vs is reacheduntil an initiatory electron appears in the high-field region toinitiate the discharge, and the formative time tf which is thetime required for the breakdown to develop once initiated. Theovervoltage is the difference (Vp−Vs)between the peak voltageVp, at which breakdown is measured, and the minimum static

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 6. IV curves for the 1024 D = 100 µm cavities arraymicro-reactor, in both anisotropic (a) and isotropic (b) cases, duringa period (f = 200 mHz, T = 5 s), in He at P = 500 Torr.

breakdown voltage Vs. The statistical time ts depends on theamount of preionization in the gap which in turn depends uponthe size of the gap and the sources producing the seed electrons.In our case, no external source exists, and the initiatoryelectrons originate only by natural external ionizing radiation,i.e. cosmic rays and natural radioactivity of materials. Therate of initiatory electron generation by such external radiationis about 4 × 10−5 electrons s−1 cm−3 Pa−1 in most gases [25].At atmospheric pressure (∼105 Pa), the electron generationrate in each cavity with a volume of about ∼10−3 mm3 isabout 4 × 10−6 s−1 which corresponds to a prohibitively longstatistical time. In the case of the 1024 cavities micro-reactor,the electrons generation rate in the volume corresponding tothe sum of the 1024 cavity volumes (which are powered inparallel) is about 103 higher. The probability for initiatoryelectron generation in the array case is 103 higher and thestatistical time ts in that case could be reduced compared withthe single-cavity case. This could induce a lower overvoltageand explain the difference of breakdown voltage in figure 7.However, that much smaller statistical time for single cavityshould be accompanied by larger error bars than for 1024cavities which is not observed. That huge difference ininitiatory electrons’ generation rate and consequently in thestatistical time between array and single case is not met in

Figure 7. Electrical characteristics of three different micro-reactorconfigurations consisting of same cavities (anisotropic,D = 100 µm, l = 150 µm): (a) breakdown voltage versus pressureand (b) V –I curves at P = 500 Torr, in helium, for f = 200 mHz.

the breakdown voltage. This could be due to the fact thatts decreases with increasing overvoltage [24]. The secondhypothesis is the possible presence of electron field emission.The voltage, just before breakdown is about 220 V for boththe 1024 and 256 microcavities array and is applied througha 6 µm thick dielectric which corresponds to an electric fieldof about 5 × 107 V m−1. The possible presence of cathodesurface ripples (scalloping) of a few tens of micrometres, dueto alternating between etching and passivation steps in theetching process [23], would enhance locally the electric fieldand could induce electron field emission. The probability ofencountering such surface irregularities might be higher inthe array case compared with the single-cavity case. Thefield emission effect could reduce the statistical time andconsequently the overvoltage by providing seed electrons.

Figure 7(b) presents the V –I curves corresponding to thethree micro-reactors. As already observed in figure 7(a), thebreakdown voltage of both array micro-reactors is similar toeach other, of the order of 220 V and much less than that of thesingle-cavity micro-reactor. As expected from the limitationof the cathode area, the discharge enters in an abnormal regimein the three cases. But this abnormal regime depends onthe configuration. It is less pronounced when the number ofcavities increases. In other words, the differential resistancecharacterizing the abnormal regime in which the first ignited

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Table 2. Geometrical features of the cavities of the twomicro-reactors (16 × 16 = 256) used for cavity opening diameterstudy; D: opening diameter, dn: distance to nearest neighbour cavity,l: depth, Scath: wall surface area (cathode surface), V : volume.

D (µm) dn (µm) l (µm) Scath (mm2) V (mm3)

100 100 150 0.055 1.18 × 10−3

150 150 150 0.088 2.65 × 10−3

discharge enters, decreases as the number of cavities increases.Moreover, the voltage drop after breakdown differs dependingon the configuration. The field emission effect by itself couldexplain as an additional electron source both observations.For exactly the same cavity features, depending on the micro-reactor configuration, the maximum current driven by a singlecavity is quite different. It is 1, 2.5 and 6 mA for the 1, 256and 1024 cavities micro-reactor, respectively. It is worth notingthat, despite exhibiting a smaller voltage drop and a larger slopein the abnormal regime than the 1024 cavity array, only onemicro-discharge in the 256 cavity array ignited. We speculatethat this could be due to the stochastic nature of gas breakdown.

3.1.3. Cavity opening diameter. Here we report resultsobtained varying the cavity opening diameter. In the caseof anisotropically etched cavities, the opening diameter isequivalent to the inner cavity diameter. The influence ofthat parameter on the electrical discharge characteristics hasbeen studied using a multi-diameter micro-reactor consistingin anisotropic cavities l = 150 µm deep. For that case, twodiameters D = 100 and 150 µm have been tested. Thegeometrical characteristics of both cavities are indicated intable 2. For surface and volume calculations, the cavity wasconsidered to be cylindrical. The corresponding breakdowncurves with respect to pressure and the I–V curves at 500 Torrare shown in figures 8(a) and (b), respectively. The breakdownvoltage curves match quite well over the full pressure range.For that type of cavity (anisotropic l = 150 µm deep),experiments show that the cavity opening diameter does notinfluence the breakdown voltage. 2D axisymmetric electricfield simulation using the finite element method (FEMM [26])shows that opening diameter does not influence the geometricalelectric field strength distributions significantly. The I–V

curves of figure 8(b) show that a single micro-discharge ignitesin both cases and the abnormal regime in which it enters doesnot depend on diameter. However, we also observed in otherexperiments, considering diameter ranging from 25 to 150 µmthat opening diameter does have an influence on ignition. Thesmaller diameter cavities tend to ignite first at higher pressureswhile bigger diameter cavities ignite preferentially at lowerpressures.

3.1.4. Cavity depth. The influence of cavity depth has beentested using two micro-reactors having the same configuration(1024 cavities arrays, diameter D = 150 µm, but withdifferent cavity depths, l = 70 µm and l = 0 µm (non-etched)). The breakdown voltage curves between 100and 1000 Torr and the corresponding I–V characteristics at500 Torr are shown in figure 9. What is quite obvious is the

Figure 8. Electrical characteristics of two 256 cavity arrays havingthe same cavity shape and depth (anisotropic, l = 150 µm) butdifferent diameters (D = 100 and 150 µm): (a) breakdown voltageversus pressure and (b) I–V curves at 500 Torr, in helium, forf = 200 mHz.

much lower (60–70 V) breakdown voltage for the non-etched(0 µm deep) cavity micro-reactor compared with the etchedone. It is approximately 160 V over the pressure range (200–1000 Torr), the curve shape being qualitatively the same as thatof the etched cavity. Some effect must compensate the higherstatistical time expected in the non-etched case due to a lowerelectron generation probability (because of the smaller cavityvolume) which should have increased the breakdown voltage.The most straightforward explanation could come from thedifference between electric field strength distribution in theetched and non-etched cases. 2D axisymmetric simulationof geometrical (before breakdown) electric field using thefinite element method [26] shows similar electric field strengthdistributions for voltage drop Vac between electrodes of225 and 160 V for the 70 µm deep and non-etched cavitiesrespectively. Figure 10 shows the electric field strengthdistribution with isovalues in the range 0–5 × 106 V m−1. Thedarker zone thus corresponds in both cases to an electric fieldstrength higher than 5 × 106 V m−1. From that plot, it canbe seen that the electric field distributions are quite similarin both cases. Compared with the non-etched cavity, 65 Vmore in voltage drop between electrodes is required for theetched cavity to obtain similar electric field distribution. Theycould consequently provide similar conditions for electronmultiplication.

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 9. Electrical characteristics of two 1024 cavities arrays withsame cavity shape and diameter (anisotropic, D = 150 µm) butdifferent depths l = 70 and 0 µm: (a) breakdown voltage versuspressure and (b) V –I curves at P = 500 Torr, in helium, forf = 200 mHz.

3.2. Operating parameters

3.2.1. Rate of the voltage ramp. All I–V curves presented inthe last sections are obtained by applying a triangular voltagewaveform to the micro-reactors and acquiring the dischargevoltage and current signals over one period. Therefore, wehave investigated the influence of the voltage rate of rise onthe I–V characteristics by varying the waveform frequency(period) while keeping the amplitude constant. Measurementshave been carried out using a 1024 array of D = 100 µmisotropic cavities as shown in figure 3(b). Figure 11 is a plot ofthe I–V curves, obtained for two different frequencies, f = 50and 200 mHz, in He at 500 Torr. Those waveform frequenciescorrespond to waveform period T = 20 s and 5 s, respectively,and voltage rise rates of 60 V s−1 and 240 V s−1, respectively.First, the number of micro-discharges which ignite dependson the voltage rate of rise. It increases with decreasing rate ofrise: three cavities ignited for f = 200 mHz while eight ignitedfor 50 mHz. The longer the waveform period, the larger thenumber of ignited micro-discharges. This can be explainedthrough the statistical generation time ts (section 3.1.2). For thesame initiating electron generation rate from natural sources(same micro-reactor configuration, same cavity volume, samepressure), the probability of appearance of electrons is higherin the case when the voltage application time is longer.

3.2.2. Pressure. To test the influence of pressure on operationof micro-reactors, we used the same micro-reactor as insection 3.2.1. The I–V characteristics have been obtainedin helium for pressure ranging from 100 to 1000 Torr fromwhich the I–V curves at two representative pressures have beenplotted in figure 12(a). Here, the waveform frequency is f =50 mHz. Only the increasing phase of the voltage waveform isshown in figure 12 (that is half the period: T/2 = 10 s) in orderto emphasize the effect on micro-discharge ignition. For thesame voltage rate of rise (same signal frequency f = 50 mHzand same amplitude), the number of micro-discharges whichignite (indicated by arrows) during that time interval varieswith pressure, more ignite at lower pressure. The time intervalbetween successive ignitions being quite constant at a givenpressure, we can speak in terms of ignition frequency. Inother words, the ignition frequency decreases as the pressureincreases as shown in figure 12(b). That tendency has alsobeen observed for anisotropic cavities. The efficiency of theionization process is known to depend on the reduced electricfield, E/n, which decreases with increasing pressure as weobserved.

3.2.3. Polarity. All the results have been obtained so farby biasing negatively the silicon (which we will term ‘direct’polarity). As we explained in section 1, the reason is it takesadvantage of the inherent limitation of the cavity surface areato force the micro-discharge to enter an abnormal glow regimeand ignite many micro-discharges in parallel. We studiedthe effect of polarization on the electrical characteristics ofmicro-reactors and the results obtained using a single cavity(anisotropic, D = 100 µm, l = 150 µm) are presented infigure 13. The breakdown voltage is clearly higher over thefull pressure range for reverse polarization. By reversingpolarities, we change the cathode from silicon to nickel. Itis known that the cathode material and topography affects thebreakdown voltage. The secondary emission coefficient, γ , ofthe material, which provides information on the efficiency ofelectron emission from the cathode due to ion bombardment,can have a large impact on the breakdown voltage [27]. Thesurface roughness of the nickel layer and silicon cavity mightalso influence the electron emission and consequently thebreakdown voltage. It is noteworthy that these results wereobtained using a previously tested micro-reactor rather thana new one. Indeed, the cathode surface topography evolveswith operation time and may give results which have somelevel of variance. A rougher surface in the used micro-reactor case could enhance the emission of electrons fromthe cathode surface through field emission, thus reducingthe breakdown voltage as observed in figure 13(a). On theother hand, we note the close correlation with figure 7(a).This indicates that the single cavity of these experimentswas not unduly affected. In addition, it has already beenshown [28] that the electrode polarity, when using non-uniformfield, could have a large influence on the breakdown voltage.Concerning the I–V characteristics, first, the two differentpolarizations give two different shapes of curves. Comparedwith the direct polarization where the discharge is clearlyin an abnormal glow regime identified by its positive slope

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 10. 2D geometrical electric field in a single cavity with diameter D = 150 µm; A (nickel), D (SiO2) and C (silicon) stand for anode,dielectric and cathode respectively; the dotted line represents the cylindrical symmetry axis; the darker zone in the electric field strengthdistribution corresponds to values higher than 5 × 106 V m−1.

Figure 11. I–V characteristics of a 1024 cavities arraymicro-reactor with isotropically etched cavity with diameterD = 100 µm (figure 3(b)) obtained in helium at P = 500 Torr fortwo different voltage signal frequencies f = 200 mHz (T = 5 s)f = 50 mHz (T = 20 s).

I–V relationship, the reverse polarity is clearly in a normalglow regime as can be seen by the nearly zero slope ofthe I–V relationship and was expected. It is due to thepossibility for the discharge, in the reverse polarity casecompared with the direct one, to spread over the cathodesurface when increasing current, keeping constant the currentdensity. Second, the order of magnitude of the maximumcurrent driven by the single micro-discharge is very differentdepending on polarities. It is approximately 20 times largerin the reverse polarity case. The dependence of secondaryelectron emission on cathode material and topography can beproposed as an explanation, but the difficulty of finding thesecondary electron emission coefficients for both materialsmakes the explanation speculative. The non-uniform electricfield distribution in the present electrode configuration couldproduce, by changing polarities, different ionizing efficiencydue to differences in charges trajectories, which has alreadybeen stated in 2D electric field distributions [28].

Figure 12. Influence of helium pressure on ignition of a 1024cavities array micro-reactor with isotropically etched cavities withdiameter D = 100 µm and depth l = 150 µm (figure 3(b)): (a) V –Icharacteristics (the arrows indicate microcavity discharge ignition:the small ones for 500 Torr and long ones for 750 Torr), (b)microcavity discharge ignition frequency, for the same voltage rate(f = 50 mHz).

4. Discussion

All breakdown voltage curves versus pressure, obtainedby varying cavity shape, diameter, depth, micro-reactor

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

Figure 13. Electrical characteristics of a single-cavity micro-reactor(anisotropic, D = 100 µm, l = 150 µm): (a) breakdown voltageversus pressure and (b) I–V curves at P = 500 Torr, in helium fordirect and reverse electrode polarization, for f = 200 mHz.

configuration and polarization have the same qualitative shape.They all present two distinct parts: at small pressures, basicallybelow 200–300 Torr, the breakdown voltage rapidly increaseswith decreasing pressure and at high pressure >200–300 Torr,the breakdown voltage remains almost constant.

Paschen [6] has shown experimentally, in the case ofparallel electrodes (uniform electric field), that, for a given gasand cathode material, the breakdown voltage Vbr only dependson the product pd (p: pressure, d: electrodes gap). We mustpoint out that the relationship Vbr = f (pd) is valid only fora given temperature and that for a more general applicability,that is to be valid in case where temperature is varying, itshould be written in terms of nd , where n is the numberdensity of gas, in order to have a temperature-independentrelationship. Here we assume that, during the measurementof the breakdown voltage, the temperature is constant, that iswe can speak in terms of pressure without ambiguity. Thetheoretical model he used to explain that dependence, basedon electronic avalanche phenomenon, takes into account twophysical processes. One is a volume process which occurs inthe electrode gap (electronic impact ionization). The other isa surface process and occurs at the cathode surface (secondaryelectron emission). Each of these processes is characterizedby a parameter, respectively the ionization coefficient (firstTownsend coefficient α) and the secondary electron emission

coefficient of the cathode (second Townsend coefficient γ )which both depend on the reduced electric field E/p. Thesecond process is necessary for maintaining the dischargesince otherwise the initial population of electrons (producedby the first process) would be quickly collected by anodeand not replaced fast enough to sustain the discharge. Thebreakdown or the self-sustaining condition depends on boththose parameters through the relation γ [m−1] = 1 where m =exp(

∫Sα(s) ds) = exp(αd) is the electronic multiplication.

Using the semi-empirical expression α/p = f (A, B, E/p)

for the ionization coefficient, where A and B are gas dependentand determined experimentally, the breakdown voltage canbe written Vbr = f (pd; A, B(gas); γ (cathode material)). Itfollows that for a given electrode system with cathode material(with a specific γ ) and a given gas (with specific A and B

coefficient), Vbr is only a function of the product pd.In the case of a parallel electrode system, the distance over

which the discharge occurs is well defined—assuming care hasbeen taken to prevent long-path breakdown for low values ofpd (which correspond to the left branch of the Paschen curve).This distance corresponds to the electrode separation d becauseelectrons will drift in the electric field direction, which in thiscase is perpendicular to the electrodes. With such a system, it ispossible to get the pd dependence of Vbr due to the possibilityto fix independently p and d.

In the microcavity case, despite a well-defined electrodeseparation which is the thickness of the dielectric, it isdifficult to define accurately the effective discharge gap d forbreakdown. The distance over which the discharge occursmight change, depending on the pressure, allowing a lowbreakdown voltage even if the pressure changes from the valuethat favours the minimum electrode spacing. Indeed, fromthe Paschen model, there exists a value (pd)min of the pd

parameter, for which the breakdown voltage is minimal. Itcorresponds to a value of the reduced field (E/p)min = B

which corresponds to an optimum electron energy giving amaximum ionization probability. Thus, the conditions forbreakdown are the easiest at (pd)min because the conditionsfor electron multiplication are optimal. For helium, in theparallel electrode configuration, (pd)min ∼ 5 Torr cm.

It follows that, in the same way, there should exist inthe present electrode configuration, a value (pd)′min providingoptimal conditions for breakdown with minimal breakdownvoltage. It means that for a given pressure p, the dischargeshould strike over a distance d such that pd = (pd)′min.The geometry of the micro-reactor used here (height of thecavity side wall) is such that the gap width over which thedischarge can ignite varies over a certain range. It means thatfor two different pressures p1 and p2 > p1 the distance d

over which the breakdown occurs can adapt itself to d1 andd2 < d1, respectively in such a way that the parameter pd

remains constant: p1d1 = p2d2 = (pd)′min permitting thelowest breakdown voltage V min

br . This should be possiblewithin a certain pressure range. In this study, that rangeis 300–1000 Torr. Beyond, limitations should appear whichwould probably induce an increase in the breakdown voltage.At a certain higher pressure, the discharge gap for breakdowncould not be reduced more, limited by the electrode separation.

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J. Phys. D: Appl. Phys. 45 (2012) 065201 L Schwaederle et al

For a pressure even higher, the pd parameter could not bekept constant and would increase, inducing, according to thePaschen model, an increase in breakdown voltage. At pressurelower than about 200–300 Torr, the observed increase inbreakdown voltage with decreasing pressure may be explainedin terms of limitation of the breakdown distance gap. Indeed,due to some geometrical limitations, d cannot further increasewhile decreasing pressure, leading to a decrease in the pd

parameter inducing, still according to the Paschen model, anincrease in breakdown voltage.

5. Conclusion

Breakdown of micro-discharges ignited in silicon cavities hasbeen studied. Different micro-reactor configurations, cavityshapes, sizes and operating conditions have been investigated.The cavity shape (whether anisotropic or isotropic) as wellas the cavity opening diameter have been shown not tobe important parameters determining breakdown voltage.No significant influence by either of those parameters wasobserved in breakdown voltage or in the I–V characteristics.In contrast, the configuration and the cavity depth have abig influence on both measurements. The delay time andelectron field emission have been proposed as explanations ofthe differences in breakdown voltage in the three investigatedconfigurations. Also, much lower breakdown voltages havebeen obtained for non-etched cavities as compared withetched cavities. As shown by finite element modelling, thegeometrical electric field distribution might enhance electronmultiplication in non-etched cavities. Moreover, changing thevoltage rate of rise or the pressure has been shown to havean impact on the number of micro-discharges that could beignited. This can be explained through arguments utilizing thedelay time and the reduced electric field, respectively. Finally,the difference in breakdown voltage and I–V characteristicobserved when inverting polarization was found to be due tothe different cathode materials and surface topography as wellas the non-uniformity of the electric field.

Acknowledgments

This work is financially supported by the French AgenceNationale de la Recherche through the contract No ANR-09-JCJC-0007-01 under the name SIMPAS project and supportedby the RENATECH network. We would like to thank CTU-IEFteam for their valuable help.

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