ISDEIV_BasicConsiderations

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BASIC CONSIDERATIONS CONCERNING LIGHTNING IMPULSE VOLTAGE

BREAKDOWN IN VACUUM

U. Schümann, M. Kurrat

Institute for High-Voltage Technology and Electric Power Systems

Technical University of Braunschweig, Germany

Abstract:In this work, theoretical considerations concerning

breakdown in the case of lightning impulse voltage(1.2/50µs) are investigated. Two breakdownhypotheses are commonly available in publication.

One is particle induced breakdown [1], where chargedparticles pass through the contact path. On contactwith the anode, the induced processes lead to voltage

collapse of the configuration. The other assumes thatthrough field emission [2] current, micro tips melt onthe surface. An explosion of a micro tip leaves behind

a micro plasma which induces the breakdown.Two breakdown types in the rear and front of thelightning impulse voltage can be recorded during

dielectric tests of vacuum gaps to determine theelectric strength.The breakdown processes should be compared

considering their physical processes. The modelshould help to clarify which breakdown mechanism ismore probable for the individual breakdown.

1.

IntroductionThe electric strength of contact systems in vacuum

strongly depends on the surface conditions. Usuallycontat systems are conditioned to get a reliable electricstrength. Many conditioning methods are known [1].

In experimental investigations with lightning impulsevoltage, as described in detail elsewhere [3], theimpulse voltage test can be used to condition thecontact systems. If the current through the vacuumgap is measured during the conditioning procedure,different impulse voltage stress types are visible.

Fig.1 shows a typical conditioning routine of theelectrodes with increasing stress. Four test cycles arepassed through whereby each time the voltage is

increased by 5kV, so that finally only breakdownoccurs.

0,0

20,0

40,0

60,0

80,0

100,0

120,0

140,0

160,0

180,0

0 50 100 150 200

U

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

p e a k v a l u e

m i c r o d i s c h a r g e

not failure

failure

micro discharge

general conditioningtide

figure 2

kV Acycle 1 cycle 2 cycle 3 cycle 4

n

fig.1: conditioning routine with impulse voltage, gap distance 5mm

Fig.2 shows the third sequence of fig.1. Typicalcurves of currents are shown in fig.3. This curvesshow the current in detail and characterize also a

breakdown caused by micro discharges. The greatestnumber of breakdowns occur in the rear of the impulsevoltage and can be ascribed to micro discharges [4;5].Fig.4 shows the electrodes after the measurement.Visible craters on the surface are observed.

80,0

90,0

100,0

110,0

120,0

130,0

140,0

150,0

160,0

125 135 145 155 165

U

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

p e a k v a l u e

m i c r o d i s c h a r g e

not failure

failure

microdischargeflow of the current

see figure 3

breakdown in the

rise time

AkV

n

fig.2: third sequence of the conditioning routine

-0,05

0,05

0,15

0,25

3 8 13 18 23 28 33

t / µs

I / m A

1 stress

6 stress

2 stress5 stress

3 stress4 stress

micro discharges

-50

0

50

100

150

200

0 20 40 60 80 100

t / µs

U

/ k V

-0,100

0,100

0,300

0,500

0,700

0,900

I / A

u i

voltage collapse

measurement range

fig.3: micro discharges (left) and breakdown process (right)

fig.4: surface of the anode and cathode after stressing (stainlesssteel)

Single breakdowns in the front of the lightning

impulse voltage appear especially after pre-stressing(fig.2). These can be interpreted by differentmechanism, which will be explained by simple

assumptions and can be proved with two models. Inthe following, these models are explained and theadaptability relating to the breakdown in the front is

discussed.

Most of the models need a higher electric fieldstrength than the homogeneous field strength U/d,

where is U the applied voltage and d the gap distance.It is possible to determine the local electric field with

XXIst International Symposium on Discharges and Electrical Insulation in Vacuum, Yalta, Ukraine, 2004


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Eloc= ßtot Ehom, where is Ehom the homogeneous fieldstrength and ßtot is the field intensification factor.Normally factor ßtot is a product of three ßtot=

ßmac•ßadd•ßloc(ϕ), where ßmac is the field intensificationfactor by the macroscopic geometry. ßadd is caused by

another physical phenomenon and is discussed

afterwards. ßloc is the influence of the microstructureof the surface [6], so that you receive for the local

field strength Eloc= ßtot Ehom as aforementioned.The parameter ßtot is determined by the Fowler-Nordheim-Plot [7]. Fig.5 shows a F-N plot for a

vacuum chamber. In addition the plot for the synthetic

micro tip defined in the following chapter is shown.

-14,00

-13,50

-13,00

-12,50

-12,00

-11,50

-11,00

0 ,000 0 ,005 0 ,010 0 ,015 0 ,020 0 ,025 0 ,030 0 ,035 0 ,040

1/U

l o g ( I / U ² )

-30,00

-29,50

-29,00

-28,50

-28,00

-27,50

-27,00

1 mm, ß=587, Ae=4.39E-18m²

2 mm, ß=580, Ae=3.30E-17m²

2 mm, ß=315, Ae2.525E-17m²

3 mm, ß=204, Ae=1.99E-15m²

3 mm, ß=203, Ae=1.38E-15m²

10 mm, ß=330, Ae=3.75E-14m²

1/kV

log(A/V2)

F-N-plot of the

synthetic microtip

failure

ß decrease

measuringsequence

l o g ( I /

U ² )

log(A/V2)

fig.5: F-N-plot of a vacuum chamber [7] and F-N-plot of the

sysnthetic micro tip (fig.6)

( )

4.526 2 9 1.5

22

1.54 10 10 6.8310

2

1log( ) log( ) ( )e

A d

d w y

I

U U

φ β φ

β φ

−⋅ ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅

⋅= − (1)

Ae: effective emission area

φ: work function (4 eV for stainless steel)

ß: total field enhancement (ßtot= ßmac•ßadd•ßloc(ϕ)

w(y) elliptic function (≅ 1)d gap distanceI total current (through the micro tip)U applied voltage

Equation (1) is the modified FN-relation, to calculatethe parameters ß and Ae. ß is detemined by the slopeof the graph and Ae by the intersection with the y-axis

2.

Electron Emission

For this theory the basic model is a cylindrical microtip with a hemispheric end and a total length of 1µmand a radius of 0.1µm. Fig. 6 shows the electric fieldcalculation for this micro tip. The homogeneous fieldstrength between the gap represents 2x107V/m(200kV/10mm).

E =2e+7 V/mh

ITip

path

0.02

2.63

5.26

7.88

10.50

13.10

15.80

18.40

21.00

23.70

x 10 V/m7

phi

fig.6: field distribution of the synthetic micro tip, 3D rotational

calculation

The electric field distribution along the path on thesurface is not constant. It is possible to determine afield intensification factor ßloc which depends upon thelocation on the path. This correlation shown in fig.7

can be expressed as a function ßloc(ϕ) (second order

polynomial approximation) of the angle ϕ (fig.6).

0

5

10

15

20

25

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

0

5

10

15

20

25

( )loc β ϕ

ϕ

E

710 V m⋅

electric field distribution

field intensification factor

2( ) 1.87 0.133 11.8loc

β ϕ ϕ ϕ = − ⋅ + ⋅ +

1/rad

fig.7: field distribution and field enhancement along the path

This approximation facilitates the solving of the FN-Equation to determine the whole current passing themicro tip by integration.

( )

( )

( )( )( )

9 1.56.831026 2

2

(1.54 )10( , )

v y

E t h

mic

E t

e micw y A

I E t e dAφ

β ϕ

φ

β ϕ − ⋅ ⋅ ⋅

−⋅⋅ ⋅ ⋅

⋅= ⋅ ⋅

(2)

The parameter ßloc varies from 12 to 7 and is not highenough to generate a current which is able to heat upthe micro tip to the melting point. The value of theintegral is near by zero. The FN-theory needs

fieldstrength higher than 3x10

9

V/m, so an additionalß-factor is required. A value of 30 for ßadd is assumed.Then a theoretical analysis sets the parametersßtot=330 and the effective emission areaAe=3.75x10

14m² at the same range as the measuredvalues (fig5). Although the field enhancement is notconstant over the micro tip´s surface the F-N-plot of this tip is a perfect straight line.Fig.8a illustrates that such microprotrusion is possible.The surface topology of a 0.3x0.25mm² section of thevirgin electrode (pre-treated mechanically with emerypaper (grade 120)) is detected by interferencemicroscopy. Fig. 8b shows an element plot of the

synthetic model from the FEM program.

a)

T_tip

T_cyl_top

T_cyl_bas

element plot

b)fig. 8: measured surface topology a), element plot of the synthetic

micro tip b)

Two basic principles of breakdown mechnism causedby field emission exist. These are the cathode and theanode response. In the following the first breakdownmechanism is discussed. Also the possibility of microparticle induced breakdown in the rise time of impulsevoltage will be discussed.


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3.

Explosive Electron Emission

The cathode response (explosive electron emission[8],[1]) is caused by a melting emitter on the cathodesurface. Four energy exchange mechanisms areimportant for the thermal situation in the micro tip:The joule heating, the Nottingham effect, thermalcooling by heat conduction and thermal cooling byheat radiation [1]. The simulation is according to fig.9and shows the course of events before the explosionoccurs.

space

discharge

electron emission

( , , , )e tot J f E T φ β =

( , ) j eW f J δ =

( , )wW f C λ =

( , ) N eW f J T =

( )r W f T = ∆

radiation

Nottingham joule heating

heat conduction

( )T κ

( )

( )

C T

T λ

T e J

e J

e J

E

energy conversion

energy loss

fig.9: simulation model, the mechanism in the grey rectangles areincluded in the simulation

The simulation includes heat conduction, joule heatingand heat reaction [9] on the field emission current inaccordance with the following equation [10]:

5

5

9.3 10( ) ( , )

sin( 9.3 10 )

T E

e eT

E

I T I E t π φ

π φ

⋅ ⋅ ⋅ ⋅= ⋅

⋅ ⋅ ⋅ ⋅ (3)

Heat conductance, heat capacity and the electricconductivity are dependent on temperature [11]. Aheating time can be calculated. Fig.10 shows the fieldemission current for different field enhancementcalculated with equation (1) and points out the strong

relation between the field enhancement and the fieldemission current.

0,00

5,00

10,00

15,00

20,00

25,00

30,00

35,00

40,00

0 0,5 1 1,5 2 2,5 3t

µs

mA

I

field emission currentequation (1)

ßtot=330

ßtot=250

ßtot=300

ßtot=400

fig.10: relationship between ß and field emission current

Fig.11 shows the temperature pattern of the micro tipat the top the base and one location between for

ßtot=330. The temperature distribution after 900ns forthe same field intensification is shown in fig.12. Thecalculated temperature is higher than the meltingtemperature. At first it seems to be curious that thetemperature on the top (T_tip) is not the highest. For

explanation the current density has the highest valuein the cross section area of the cylindrical part of themicro tip.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0,7 0,75 0,8 0,85 0,9

t

µs

T

K

T_cyl_top

T_cyl_bas

T_tip

ßtot=330, Ae=3.75E-14m²

fig.11: temperature curve at the top and at the base of the cylindricpart and on the top of the hemispherical part of the micro tip

293.00

2017.0

3742.0

5466.0

7191.0

8915.0

10639

12364

14088

15813

T_tipT_cyl_top

fig.12: temperature distribution at 0.9µs, ßadd=30

At 900ns the inversion temperature Ti=5.4x107E(t)φ-0.5

is lower than the temperature of fusion (for stainleessteel=1835 K), so a breakdown could occur [1]. The

whole mass of the synthetic tip is 2.37x10-16

kg [12], asecond indication for the possibility that a breakdownoccurs in the front ramp even if we take into account

the building up time for the plasma

(tpl=d/vpl=0.01/2x10

4

s=500ns,[13],[1]). For a smallerßadd less than 30 the micro tip does not reach themelting temperature (fig.10), with the result that aadditional field intensification factor is reallynecessary.

4. Model of a micro particle induced breakdown

Basically there are two different types of

microparticles on the surface. There can be metallicparticles, e.g. loose metallic melting drops comingfrom a previous voltage stress. In other cases micro

tips can be seperated by the force of electrical field[6]. But also non metallic will be found. Fig.13 showsa metallic particle on the surface of an electrode.

To cause a breakdown in the front of the impulsevoltage a particle has to transit through the gap in oneor less then one microsecond (fig.13).

rßadd

plasma

p

t trplt

tsep


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This transit time ttr depends on the local field strength,for spherical metallic particles you achieve thefollowing relation between the particle charge and the

local electric field [6].

( )20( ) 6.6 p sep p sep add q t r E t ε π β = ⋅ ⋅ ⋅ ⋅ ⋅ (4)

The following equations allow to determine the transit

time for a charged spherical particle with radius rp (of stainless steel).

34 p p p pV r m V π ρ = ⋅ ⋅ = ⋅ (5),(6)

10.965 69 0.395

( ) (exp( ) exp( ))sep sept t U

sep sep add add d µs µs E E t β β = ⋅ = ⋅ − − − ⋅ (7)

( ) ( )el p sep sep p inertiaF q t E t t m a F = ⋅ > = ⋅ = (8)

Fig. 14 shows the breakdown time tb= tsep+ ttr+ tpl andthe anode velocity of a particle (mass density of theparticle is 7800kg/m³). Seperation time tsep and also

the additional field intensification factor ßadd have abig influence on transit time ttr for a gap distance of 10

mm and a peak voltage of 200 kV.

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200

0

500

1000

1500

2000

2500

3000

3500

4000

Esep=0.25 U/d

Esep=0.5 U/d

Esep=0.8 U/d

tb

ßadd

vp

µs m/s

Esep

Esep

8 550m scv σ

ρ =

fig.14: velocity at the anode and point of time when the breakdowncould occur. In all cases tb is greater then 2µs (rp=500nm).

Even a very small particle with a radius of 10 nm anda ßadd of 200 transits the gap fast enough. WhenEsep=0.5 U/d the breakdown transit time is about 1.3µs

The velocity at the anode [14] is in the range of thefivefold critical velocity (equation (9)) so the particlecould evaporate and breakdown time tb (1.8µs) lies in

the rise time of the impulse voltage.

8 550 m scv σ

ρ =

(9)

σ is the tensile strength, ρ is the mass density.

5. Results and discussion

T>0

coulomb-wall

thermoemission

metal vacuumsemiconductor

valence

band

quantumwell

conduction

band

hot-electronseU e U

d

distance

potential energy

fermi level

fig.15: energy band configuration of a composite microregime. The

middle layer is semiconducted [15]

Under the assumption that electron emission or a

particle caused a breakdown in the rise time a fieldenhancement ß is needed which is greater than the

local field enhancement caused by the particle or bythe micro tip alone.Some phenomena are noted which indicate a very high

ß-factor. For example fig. 15 shows the energy bandconfiguration of a layered microstructure of metal-semiconductor-vacuum [15] As per the following

relation:9 0.54.56 10

r

d add ε β χ

∆= ⋅ ⋅ ⋅ (10)

It is possible to explain high ß-factors in the rangefrom 100-10000. The phenomenon is called Schottky-Emission. Electrons in the valence band of the

semiconductor layer get kinetic energy under theinfluence of external high electric field. These hot

electrons are able to negotiate the potential barrier χ.This phenomenon produces the same relation between

field emission and voltage stress, but the fieldenhancement has another physical cause.To get high ß-factors without other phenomena the

micro tip must have other geometrical conditions. Thegeometrical ß-factor follows the relation ß≅2+h/rwhere h is the total length and r the radius of the tip[6]. To receive high ß factors up to 300 the ratio h/rmust also be near 300, too, but this tends to result in

unstable mechanical micro tips.A particle with a radius of 0.5µm needs a ßadd of 10000 to force a breakdown in the rise time of the

lightning impulse voltage, but it is not generallyexcluded that a particle can be the reason for abreakdown for example in the back of impulse stress.

5. References

[1] Latham, R.V.: „High-Voltage Vacuum Insulation – Basic

Concepts and Technological Practise“. Academic PressLondon, 1995.

[2] Fowler, R., Nordheim L.: „Electron Emission in IntenseElectric fields“. Proc. Roy. Soc., Vol.119, pp.173-181, 1928.

[3] U.Schümann, M. Budde, M. Kurrat: „Capacity influence onbreakdown voltage of electrode arrangements in vacuum“.

XIIIth International Symposium on High Voltage Engineering,Netherlands, 2003.

[4] Yen,Y.T.;Tuma, D.T.; Davies, D.K.: „Emission of electrode

vapor resonance radiation at the onset of impulsive breakdownin vacuum“. J. Appl. Phys., Vol.55, No.9, pp.3301-3307, 1984.

[5] Nevroski, V.A.; Rakhovski, V.I.: „Electrode material release

into a vacuum gap and mechanism of electrode breakdown”. J.

Appl. Phys., Vol.60, No.1, pp.125-129, 1986.[6] Rohrbach, F.:Report Cern, NTIS, 1971.

[7] S. Giere: „Vakuumschalttechnik im Hochspannungseinsatz“.Thesis, TU-Braunschweig, 2004.

[8] Mesyats, G.: „Explosive Processes on the cathode in Vacuum

Discharge”. IEEE Transactions on Electrical Insulation, Vol.EI-23, No.3,pp.218-225, 1983.

[9] Dolan, W.W., Dyke, W.P., Trolan, J.K.: Phys. Rev., 91, 1054-

7, 1953.[10]Murphy, E., Good, R.: „Thermoionic Emission, Fiel Emission,

and Transition Region”. Phys. Rev., Vol.102, No.6, pp. 1464-

1473, 1956.[11]VDI-Wärmeatlas, Berechnungsblätter für den Wärmeübergang,

VDI-Verlag GmbH, 1988.

[12]Mesyats, G., Putschkarjow, W.: „Mikroexplosionen an Metall-

oberflächen”. Wissenschaft in der UdSSR, Heft 2, pp. 48, 1987.[13]Mesyats, G., Proskurovsky, D.: “Pulsed electrical discharge in

vacuum”. Berlin, Heidelberg, New York: Springer-Verlag

1989.[14]Cook, M.: „The science of high explosives“. New York:

Reinhold 1958.[15]Eichmeier, J., Heynisch, H.: „Handbuch der Vakuumelektro-

nik”. R. Oldenbourg Verlag München Wien, pp 124–131, 1989.

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ISDEIV_BasicConsiderations