IEEE Transactions on Dielectrics and Electrical Insulation Vol. 4 No. 1, February 1997 135

High-field Single Electron Emission Rates and their Influence on the Paschen

Characteristics in Compressed Gases A. E. Guile, M. A. Salim and A. E. D. Heylen

Department of Electronic and Electrical Engineering, University of Leeds, West Yorkshire, UK

ABSTRACT By means of a newly developed statistical avalanche counting technigue which enables high-field, single electron emission rates (SEERS) to be measured from unsparked fresh- ly prepared surfaces having various thicknesses of oxide film, it is established for the first time that SEERS increases, for a given electric field, with an increase in the bulk modulus (hardness) of the material cathodes; also remarkably the thicker the oxide layer, the higher the SEERS. These trends are reflected in the Paschen sparking characteristics which show that the gaseous electric strength decreases with increase in the bulk mod- ulus and increase of oxide layer thickness of the cathode material; and thus the increase in SEERS. This former trend is opposite to that established more than forty years ago. Other hitherto unobserved phenomena like a gas pressure effect, switching from a low to a high electron emission mode and vice versa , the influence of deliberate sparking and the total absence of spark conditioning are reported. Analysis of SEERS by the more suc- cessful Richardson-Schottky rather than the Fowler-Nordheim equation shows that the low electric field intensification factors derived increase with the bulk modulus of the cathode material and ultimately are determined by the polishing procedure.

1. INTRODUCTION law begins to occur at fields of the order of 10 to 20 MV/m (10 to

EFORE the turn into this century, Paschen had already discovered B that the uniform field sparking voltage V, of gases is determined solely by the product of the inter-electrode gap distance d times the gas pressurep at a fixed temperature. This constant pd means that the total number of molecules contained between the electrodes (per unit area) and thus the quantity of insulation is constant; with increase in pd, the sparking voltage rises due to an increase in the quantity of insulation material to give the Paschen characteristic. Subsequently Paschen’s law (sometimes known as the similarity principle) has been found to apply for non-electron attaching gases to pd values in the medium range with departures from this law occurring at both small and large pd.

At small pd , say at low gas pressure, the departure is due to the ionizing electrons crossing the gap, not quickly reaching a constant average ionization energy, whilst at extremely small pd, towards the vacuum regime, the sparking voltage, which increases less than that given by Townsend’s equation, is influenced by strong field electron emission, the electrons producing hardly any ionizing collisions 111.

At large pd, say in compressed gases with which we are concerned here, the departure from Paschen’s law is strongly dependent on the condition of the electrode surface, particularly the cathode, and on gas cleanliness. In this pd region, large sparking voltages result and con- sequently high electric fields are attained; departure from Paschen’s

20 kV/mm) for electrodes prepared under standard laboratory condi- tions [2] . The magnitude of these electric fields E in compressed gases corresponds to those which lead to breakdown in vacuum and conse- quently it is natural to postulate, as for instance the authors [l] have done, that electric field emission of electrons from the cathode plays a significant role in determining compressed gas breakdown voltage levels, which it does in vacuum. It is the purpose of this paper to con- firm this hypothesis by presenting results of the dependence of high electric field single electron emission rates (SEERS) on the applied elec- tric field E for a variety of cathode materials and their various oxide layer thicknesses, and to show how these materials and their oxide layer in turn influence the Paschen characteristic obtained in various compressed gases.

In their classic pioneering work of over forty years ago, Trump, Cloud, Mann and Hanson [3] discovered, using dc voltages to 900 kV and uniform field gap distances between 5 and 20 mm, that in gases compressed up to - 2.5 MPa, the sparking voltage becomes cathode material dependent when the electric field reaches N 15 MV/m at which the breakdown characteristic starts to fall below that given by Paschen’s law. They concluded that this effect

“must come primarily from the cathode surface and consists of photo-electric, secondary and high field electron emission. High field electron emission must

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136 Guile et al.: High-field Single Electron Emission in Compressed Gases

be regarded as a probable mechanism even at gra- dients of 15 MV/m since the average is increased by localized projections and since the surface is nec- essarily contaminated by relatively low-work-function material.”

The most significant contribution to the experimental study of SEERS in the presence of a gas was made by Llewellyn Jones et al. [4,5]) who showed that SEERS as large as lo5 e/s could be attained at an electric field as low as 3.7 MV/m, in contrast to the much higher predicted theoretical field given by Fowler and Nordheim 161. Anal- ysis of their results by means of the F/N equation yielded work func- tions for the metal cathodes used, well below the accepted norm and surface emission areas of atomic dimensions rather than that of the broad area sample. Also, no trend with regard to the very small differ- ences detected in their SEERS of the numerous metals examined could be observed and this no doubt is due to the experimental technique employed by these workers, who sparked the surfaces fifty times per second so that the individual nature of the surface was obliterated and the underlying metal was reduced to an amorphous mass. Fur- ther, the applied electric field could only be varied by 25% so that it was possible to interpret the results with more success in terms of the alternative Richardson-Schottky field aided thermionic emission theory [7].

Recent Paschen characteristics for air at atmospheric pressure pub- lished by CIGRE (1977) show departures from Paschen’s Law to occur at an electric field of 15 MV/m for big gaps (50 mm) and 30 MV/m for small gaps (1 mm) [26].

A new, non-destructive, quantitative method of measuring SEERS was developed by the authors [8], which involves the pulse height analysis of statistically varying prebreakdown giant electron avalanche sizes so that sparking of the freshly polished cathode surfaces is com- pletely eliminated and singly emitted electrons can be counted, as briefly outlined below. This technique was heralded in its qualita- tive aspect in 1978 [9] when it was shown that indeed no field elec- tron emission occurs at electric fields up to 6 MV/m. Results using a crude quantitative method of this technique [lo] showed that for ac- cidentally sparked surfaces on rare occasions, electron emission only commences at 8 MV/m for copper cathodes. It will now be shown that for well-polished surfaces, SEERS (w 3 e/s) only commence at an electrical field at or exceeding 15 MV/m, depending on cathode material.

2. ASPECTS OF STATISTICAL COUNTING OF ELECTRON

EMISSION RATES.

Kojima and Kato [ l l ] and Cookson et al. [12] confirmed experi- mentally the theory of Wysman [13] and Legler [14] that between two parallel plate electrodes across which a voltage is applied, sufficient- ly high to cause ionization, the number N ( n ) of resulting electron avalanches larger than n electrons is given by the negative exponen- tial relation

N ( n ) = No exp(-n/fi) (1)

Table 1. Cathode materials used and their oxide layer thicknesses.

Cathode matl. Oxide thickness, nm

OFHC Cu CO”. c u A1 99.99% Comm. A1 2-3

Natural grown

1 :steel 1 1 170 1 380 1 1 1 p-Si 2-3 20-30 50-60 100 200

for No electrons emitted from the cathode and in which the average size of the avalanche f i is given by

fi = exp(ad) (2) where a is Townsend’s primary ionization coefficient and d the in- terelectrode gap distance. A semi-logarithmic plot of N ( n ) vs. n enabled these workers to obtain ?i from the slope of the straight line and thus the coefficient a in which they were primarily interested. If this statistical counting is performed per unit time, i.e. lJ(n), then a similar plot yields &, the number of emitted electrons per second, for n = 0, i.e. the intercept when the straight line is extrapolated back to zero. This is the basis of our original method [lo].

1000

-8 -7

e120 8

100 -

2

i

10 -

1 I I

0 160 320 v (mv) 480 640

Figure 1. Single electron emission rates (SEERS) per 20 s vs. discrimi- nator voltage for freshly polished niobium (2 to 3 nm thick natural oxide layer) for the following voltages at 0.4 to 0.8 mPa gas pressure for an inter-electrode distance of 0.5 mm: (1) 8.4 kV, (2) 9.0 kV, (3) 9.6 kV, (4) 10 kV, (5) 11.2 kV, (6) 12.2 kV, (7) 12.8 kV, (8) 13.2 kV giving SEERS (1) 0.76, (2) 2.7, (3) 4.8, (4) 10.0, (5) 20, (6) 23, (7) 33, (8) 50e/s.

A major precaution that has to be taken is to ensure that the single electron avalanches are not accompanied by secondaries and this the previous workers 1121 accomplished by carrying out measurements well away from the sparking threshold; however then exp ad E lo3 is fairly low and special low noise amplifiers had to be used. This

IEEE Transacfions on Dielectrics and Electrical Insulation Vol, 4 No. 1, February1997 137

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3. EXPERIMENTAL IMPLEMENTATION

In practice it was found possible to count electrons N 20% below the sparking threshold, so that the occurrence of sparking is complete- ly avoided; in fact SEERS can now be determined at different voltage levels for one given gas pressure. Previously, measurements had to be made within N 3% of the sparking voltage.

The electrodes were parallel plates of 1.4 cm diameter with 0.5 mm radius rounded edge. The anode was brass whilst the cathode was of various materials as listed below. The HV could be raised to 20 kV and the gas pressure to 1.3 MPa. The electrode gap distance was set to the low value of 0.5 mm so that for a given voltage, a large electric field exists between the electrodes.

Commercial and oxygen free high conductivity copper (OFHC), commercial and pure (99.999%) aluminum, mild steel and stainless steel were chosen as cathode material together with niobium for which the electronic band structure has already been well defined 1171. p-Type silicon was also included because of its modern impor- tance in semi-conductor devices (Table 1). A scratch free, mirror like finish, flat to within 50 pm overall was obtained following a three stage polishing procedure as detailed below. Since it already had come to light for copper that the SEERS are dependent on the oxide thickness [lo], this was further investigated by oxidizing the various cathodes to different oxide thicknesses using a dry or wet technique appropriate to each material (Table 1).

3.1. SURFACE PREPARATIONS

deep scratches from machining were removed by polishing with successive finer grades of silicon-carbon paper from 200 down to 600 grit size, except for pure Al, down to only 400 grit. (a) soft materials (commercial Cu, commercial Al, OFHC cop- per) were polished using successively fine grades of alumina powder (2, 0.3, 0.05 pm) with distilled water on a horizontal rotating wheel (80 rpm) fitted with removable soft leather laps. (b) very soft A1 (99.999%) as above, but 0.05 pm alumina pow- der omitted; (c) the harder materials (stainlees and mild steel) are polished with successively finer diamond paste (6, 3 and 1 pm) followed by 2, 0.3 and 0.05 pm alumina powders. (d) the very hard material (niobium) was further polished with Sic paper (grit 800); then with the usual range of alumina powder. A high degree of final finish was obtained using a vibrating plate (30 vibrationds) fitted with leather laps and soaked with a thick substance of 0.05 pm alumina powder with viscous ethane diol rather than distilled water; this gave an absolute- ly scratch-free surface. The electrodes were finally washed in tetrachloroethane and quickly dried by gently pressing on a soft tissue and blowing dry air.

Approximately 30 min to 1 h were spent on each polishing stage for every grade of alumina powder/diamond paste. This usually pro- duced a good scratch free surface; very fine scratches, introduced by uneven pressure when polishing, were removed in the following stage. The very hard Niobium took a few days per sample to polish.

138 Guile et al.: High-field Single Electron Emission in Compressed Gases

I"

16 l8 MVfm2O 22 24 (0) 0

14 Figure 3. Electron emission rate, scales A and B in e/s vs. electric field for various materials as follows (1A) Pure A1 (2 to 3 nm); (2A) pure A1 (20 to 30 nm); (3A) pure A1 (50 to 60 nm); (4A) Cu, OFHC (2 to 3 nm); (5A) p-type Si (2 to 3 nm); (6A), Cu (OFHC) (20 to 30 nm); (7A), Cu (OFHC) (380 nm); (8A) commercial Cu (2 to 3 nm); (9A), CO". Cu (100 nm); (lOA), comm AI (2 to 3 nm); (l lB), stainless steel (2 to 3 nm); (128) mild steel (2 to 3 nm); (13B) niobium (2 to 3 nm); (14B) mild steel (170 nm); (15B) mild steel (380 nm); (16B) niobium (20 to 30 nm); (17B) niobium (100 nm); (18B) niobium (200 nm)

3.2. GROWING OF OXIDE LAYERS 1. Dry technique: Cu, mild steel and stainless steel were oxidized

in an oven at a fixed temperature and time, to produce the nec- essary oxide layer and thickness.

2. Wet technique (Anodization): A1 and Nb were oxidized in a bath filled with 0.1 M ammonium citrate solution using a con- stant current method. For a fixed saturation voltage, the thick- ness depends on the duration of the current at the saturation voltage.

4. RESULTS AND OBSERVATIONS

4.1. S E E R S

A typical sample, from the countless measurements made for var- ious metals, of the electron count rate N(v) above a given discrim- inator voltage, plotted against discriminator voltage U is shown in Figures (1) and (2) for two extreme thicknesses of oxide layer on nio- bium, which yielded the highest electron emission rate of all cathodes tested. In conformity with Equation (3), the results lie sensibly on straight lines with varying slopes determined by the average ioniza- tion according to Equation (2), which depends on the applied voltage and gas pressure. Both Figures show that the electron emission rate, given by the intercept of the lines on the ordinate, increases strongly with increase in applied voltage and therefore applied field. Compar- ison between the two Figures shows that the thick oxide of niobium

yields an emission rate - 5 to 10x larger than the thin oxide lay- er for comparable or even somewhat smaller voltages. As a typical comparison, h e 4, taken from Figure 1 and shown dotted on Fig- ure 2, indicates the marked increase in SEERS (9.5 x in this case) in going from a 2 to 3 nm oxide to a 200 nm oxide layer when contrasted with line 5, both taken at 10 kV. Similar results were obtained for all other materials tested having various thicknesses of oxide layer, and the derived results reproducible to within 90% are comprehensively illustrated in Figure 3.

From Figure 3 it is seen that for the vast majority of materials, elec- tron emission now only commences at electric fields ranging from 15 to 20 MV/m, in contrast to our 8 MV/m for copper when there had been some prior sparking. Further, the SEERS value is much less than before, despite the higher fields. For instance, for OFHC copper having an oxide thickness of 2 to 3 nm (natural thickness), the previous rate was 244 e/s at 20 MV/m; now it is only 1 e/s. This may be partly due to the greater care taken in preparing the samples but, more particu- larly, the complete elimination of sparking. It is observed, considering the natural oxide thickness (2 to 3 nm), that SEERS increase in going from pure aluminum, OFHC copper, copper commercial, aluminum commercial, stainless steel, mild steel to niobium. p-Type silicon fol- lows a somewhat different characteristic. Also from Figure 3, as has been mentioned before, for each material, SEERS, at a given field, in- crease with increase in oxide layer thickness.

Llewellyn-Jones etal. [4,5] reported very stable SEERS at their large values of lo5 e/s and this was expected in our case, with the complete

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 4 No. 1, February1997 139

12

9.-

els

elimination of sparking and the great care taken in producing mirror like surface finishes, that steady SEERS should occur. It was found however that with increase in electric field above SEERS' onset, the currents became less stable and could switch suddenly from a low emission mode to a high one and back again, near to breakdown, as illustrated in Figure 4. Whereas for softer materials like aluminum this switching behavior is transient and the duration of high SEERS is of the order of a second for thin oxides and increases to - 5 s with increasing oxide thickness, for harder materials like steel and particularly niobium, the duration could increase to - 1 min for thin oxides, becoming almost continuous for thicker ones; thick oxides of harder materials could switch to a high mode and remain there for a considerable period of time and then suddenly decay rapidly to a lower mode.

Figure 5 shows a gas pressure effect in SEERS whereby, if SEERS counts are made at one pressure and the pressure is then raised to a higher one and then reduced to the original one, the SEERS value is less than that observed before. If the pressure is again increased to the higher value, the same reading to within 90% is observed as before. If SEERS contribute to spark breakdown, then this should result in a hysteresis curve for the Paschen characteristics as reported further on. This pressure effect points to porosity of the oxide layer.

The increase in SEERS with number of sparks is shown in Figure 6. The decay in SEERS follows an exponential law. As given below in the Paschen characteristics Section 4.2, little or no spark conditioning was observed, probably because of extreme care taken in polishing the cathode materials, and the low energy dissipated in the spark.

-

360

280

els

200

120

40

I 28

0

25 26 E W l m ) 27 24

Figure 4. Channel 6 (240 mV discriminator voltage), electron count rate vs. electric field E showing switching from graph (1) to (2) and back again at 0.8 mPa gas pressure for niobium (20 to 30 nm oxide thick- ness). Graph (l), ignoring switched pulses; graph (2) taking into account switched pulses

*1 /' B

14 14.8 15.6 16.4 mim 17.2 18 18.8

Figure 5. Channel 6 (240 mV discriminator voltage), electron count rate vs. electric field for Cu (OFHC) (2 to 3 nm). Curve (1) at 0.4 mPa bar; (2) gas pressure increased to 0.5 mPa; (3) pressure reduced to 0.4 mPa (4) finally pressure increased to 0.5 mPa.

6

5

40

30

els

20

10.

0

x - x

0 - 0 I I

20 40 T (s) 60 80

Figure 6. Channel 6 (240mV, discriminator voltage) electron count rate vs. time T for pure A1 (99.999) (2 to 3 nm oxide thickness) at 0.4 mPa gas pressure. 0, after 1 spark; x after 2 sparks.

4.2. PASCH EN CHARACTER1 STI CS

If high field SEERS contribute to the sparking process, then Paschen characteristics should be different for different cathode materials, having the same oxide thickness. This is shown in Figure 7 for a

140

21

vs

18

15

12

9

6

3

a / b

I I I I 2.4 4.0 pd 5.6 7.2

Figure 7. Sparking voltage in kV as a function of gas pressure times gap distance in bar mm for cathodes: 0 pure (99.999%) aluminum; 0 commercial aluminum; x stainless steel. Oxide layer layer thickness 2 to 3 nm; curves 1 , 2 and 3 in nitrogen t 10% ethane gas; curves (a), (b), (c) in nitrogen.

nitrogen-ethane gas mixture where the largest sparking characteris- tic is achieved with the pure aluminum cathode which was shown to give the lowest SEERS whilst stainless steel has the lowest strength, its SEERS being much larger than that of commercial aluminum, the latter occupying an intermediate position in the graphs as expected from its SEERS characteristic; at high p d , the Paschen curve for stain- less steel (SS) bends over considerably. In nitrogen, the same sequence is maintained but now the curve for SS comes closer to that for com- mercial A1 at high pd. In air at high pd, as shown in Figure 8, the graph for SS has come very close to the one for commercial AI and at the highest p d values recorded, the sparking value for the SS cathode exceeds that for commercial Al. It was not possible to show these nine graphs on a single figure, because the characteristics intermingle but, taking the medium characteristic for commercial A1 as a reference, the dependence of the Paschen characteristic on the gas used is shown in Figure 9. At low pd , air has the lowest strength; at medium pd it oc- cupies an intermediate position and at high pd, it is catching up with the characteristic for nitrogen. In the case of pure Al, the results were similar, but at high pd the electric strength of air actually exceeded slightly that of nitrogen. Interestingly, the Paschen characteristic in the gas mixture is well below that for pure nitrogen 1251.

For the same cathode material, it was shown that the thicker the ox- ide layer, the higher is SEERS. Thus a thick oxide of a given material

Guile et al.: High-field Single Electron Emission in Compressed Gases

21

vs

18

15

12

9

6

3

P

I I I I 0.8 2.4 4.0 pd 5.6 7.2

Figure 8. Sparking voltage in kV as a function of gas pressure times gap distance in Pamx for air for cathodes: 0 pure (99.999%) alu- minum; 0 commercial alummum; x stainless steel. Oxide layer thick- ness 2 to 3 nm.

should yield a lower Paschen curve than for a thin one. This is borne out for example in the case of a OFHC copper cathode for a nitrogen- ethane gas mixture in Figure 10 where the difference between the curves commences at N 24 MV/m. For mild steel in nitrogen-ethane gas the difference in the characteristics for a thin and a thick oxide commences low down at 18 MV/m and at high pd is more marked than for copper, as shown in Figure 10. The two above mentioned elec- tric onset fields correspond to those given in Figure 3, thus showing the influence of SEERS on the Paschen characteristics. For nitrogen gas and the Cu (OFHC) cathode, the difference in the curves due to the different oxide thickness is present almost at the start as shown in Figure 9. This early difference can be attributed to a much larg- er unsuppressed secondary photon ionization coefficient for the thick oxide layer than for the thin one.

If the 2 to 3 nm OFHC Cu in nitrogen curve (a) shown dotted in Figure 9 is compared with the one for 2 to 3 nm commercial Al, then a remarkable lowering of electric strength is noticed amounting to 13% at pd = 400 MPa m at which, from Figure 10, SEERS has not yet commenced. This again must be attributed to unsuppressed photon secondary ionization, the coeffficient of which is 28 x greater for OFHC Cu compared with that for commercial Al, based on a calculation using the primary ionization coefficient for Nz given in [25]. This may help to explain why arc welding is much easier for Cu than for

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 4 No. 1, February1997 141

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Figure 10. Sparking voltage in kV as a function of gas pressure times gap distance in Pa.mx lo-' for nitrogen tlO%ethane gas for oxygen free high conductivity copper cathode with oxide thickness. 0 2 to 3 nm; 0, 380 nm; mild steel 2 to 3 nm; x 170 nm.

oxide (reaching 18% at 720 MPa m). This may again point to poros- ity in the oxide layer and/or absorbtion of water, especially in the thick one, presumably because the electrons become attached to wa- ter molecules.

5. ANALYSIS OF RESULTS AND

5.1. MECHANICAL VIEWPOINT

From extended experience over many months with the polishing of the materials and with the measurements, an innate feeling emerged that the harder the material, the larger the SEERS. To investigate this trend, all the cathode materials were tested for hardness on a Vick- ers machine. The results are shown in Table 2, where the materials used are listed in rank order according to increasing SEERS. It is ob- served that, going down this Table, this list does indeed follow the sequence of increasing Vickers hardness numbers, except for niobium and silicon. However, from experience in polishing, niobium should be similar in hardness as SS. This is vindicated by the boiling point temperature, shown also in Table 2 for most of the materials. The work function, which dominates the F/N equation, shows no clear trend. Silicon is difficult to classify as its Vickers hardness number varies over a wide range because this material is so brittle; also its SEERS (Figure 3) is unusual as it gives a larger value than most metals at low to medium electric fields; at high fields, its SEERS fall between those for pure A1 and Cu (OFHC) and so does its boiling temperature.

DISCUSSION

142 Guile et al.: High-Geld Single Electron Emission in Compressed Gases

Table 2. Material tested and physical constants: bulk modulus B, Young’s modulus Y . Emission increases from A1 through Cu to Nb. As measured

B

7.22

13.1

Pa

9.89

16.8 17.0

Matl. B V incr. SEERS 10-~ Pa Al99.999% 1.46

p-Si 6-12 OFHC c u 4.45 commcu 9.73 commAl 11.2

ss 14.5 mild steel 22.2

Nb 7.46

v I

31 I I i I 2.4 4.0 pd 5.6 7.2 0.8

Figure 1 1. Sparking voltage in kV as a function of gas pressure times gap distance in Pa. mx10d2 for nitrogen +lo% ethanegas for mild steel cathode 0; increasing for pressure x, decreasing gas pressure 0, in- creasing gas pressure again. Curve (1) 2 to 3 mi; curve (2) 170 nm.

Further insight may be gained by considering the parameters which characterize the elastic property of bulk polycrystalline ma- terials, namely Young‘s (elastic) modulus Y , the shear modules p, Poisson’s ratio 0 and the bulk modulus B, which is the inverse of the compressibility. Values for Young’s modulus are shown in Table 2, where the elements are Iisted according to increasing SEERS. The mag- nitude of Y as well as p depends on the electronic configuration of the element i.e. the group in the periodic Table in which it lies. The Y constants (and 1-1 since Y N 2.61-1) fit the sequence except for niobi- um. Poisson’s ratio is given by o(Y/2p) - 1 and it was noted more than a century ago that this ratio is approximately constant for most elements at - 0.33 so that little can be gleaned from tlus. The bulk modulus has been measured more extensively than any other elastic

Q,

eV 4.19 4.75 4.51

4.16 4.37

2480 2480 2583 12.4

2889 21.0 4540 I 10.5 I

I I I I 7.2 4.0 pd 5.6 0.8 2.4

Figure 12. Paschen characteristics in nitrogen showing effect of expo- sure to air 0, original run x, after system evacuated, sample cathode exposed to air for 30 min and then graph taken for increasing nitrogen pressure 0, graph for second run without air exposure; (a), (b), (c) Cu cathode, 2 to 3 nm; 1,2,3, Cu 380nm.

property, mainly by Bridgman, where B = Y / [ 3 ( 3 - Y / p ) ] and these values are shown in Table 2. It is seen that this modulus fits the sequence perfectly, although the value for Nb is not much larger than that for iron, but it must be stated that mild steel rather than iron was tested for its SEERS. The large Y / p = 2.80 ratio lifts Nb above Fe.

5.2. ELECTRICAUELECTRONJC

Original SEERS as a function of the electric field and for various oxide tlucknesses are given in Table 3 for the two extreme materi- als tested, viz. AI which has the lowest SEERS and Nb which has the highest. These values are derived from typical graphs as shown in

VIEWPOINT

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 4 No. 1, Februaly 1997 143

Figures 1 and 2 according to Equation (3). For a given electric field and oxide thickness, the SEERS for Nb is 2 to 120x higher than that for Al. Since previous work [4,5,10] has examined the results in terms of a fundamental model (The Fowler-Nordheim equation) with an ide- alized surface [6] it would have been useful initially to compare the results given here in terms of that model, but as mentioned earlier, this interpretation gives impossible values in the work functions and emission area; so now the authors invoke the much more reasonable Richardson-Schottky field-aided thermionic equation.

A more rewarding interpretation of high-electric field electron emission is by the Richardson-Schottky formula [7] in which the SEERS value N+, is given by

(5) 120T2 0.44M0.5E0.5

T N-,= -Sexp [z] +

e

where e is the electronic charge, S = 1.54 cm2 the sample area, T the absolute temperature, k Boltzmann's constant and E the electric field in V/m. The first original exponential Richardson term neglects the lowering of the work function Q by the electron image force relative to the metal surface and the second Schottky term takes this into account. Thus a plot of In& vs. should produce a straight line with an intercept yielding the work function and a slope giving the field intensification factor M .

Table 4. Work function (9) and electric field intensification factor M for three material cathodes having various thicknesses of oxide film (see text).

mi 50-60 1.67 1.15

I 2.43 [ 76.8

present SEERS, but typical graphs, given in Figure 13, show that it holds now within the scatter of the data. With regards to the latter, it is worth pointing out that the higher the SEERS, the steadier the individual results, except when switching occurs. Thus Llewellyn- Jones etal. (1953) obtained extremely steady SEERS for a given applied electric field; our previous results [lo] were fairly steady (within 3%), but now at low SEERS, Figure 13 shows quite a bit (within 10%) scatter in the experimental data.

The deduced work functions and field intensification factors de- rived from Equation (4) for Nb and Al, are shown in Table 4 together with those obtained for Ni from the data of Llewellyn-Jones et al. [4,5]. It is seen that the values for work function are reasonable, though somewhat on the low side, and that the electric field inten- sification factor M is understandably lower for our data than those of Llewellyn-Jones; also M for Nb is much less than for Al. McAllis- ter and Vibholm [28] obtained M = 6.6 for sandblasted electrodes, but the material is not specified.

It is postulated that harder materials cannot yet be polished as smoothly as softer materials and this gives a link, through M , be- tween our mechanical and electrical/electronic viewpoints outlined above. Tallysurf measurements (tip radius 2 pm) of the surface as- perities, up to a sensitivity of 10 nm/mm of graph paper confirm this, showing Nb to have more jagged asperities than Al, the latter reveal- ing more gently undulating cross section profiles.

For many decades, researchers into compressed gas and vacum in- sulation/failure have calculated from their experiments that the elec-

cathode surface, reached values exceeding 300; our results show, for the first time, very modest values in the range 1.0 < M < 7.5. This agrees more with the highly mathematical work of Lewis [27] who calculated that, for ideal but realistic asperities such as a simple prolate hemispheroid on a plane or a system of uniform neighboring rigdes each having a semi-elliptic crosssection, the average intensi- fication factor M n/ 3.0, almost exactly as Schottky has calculated before for a hemi-spherical boss on a smooth surface.

1 0 3 - 8 - f

6 - e

4 -

2 -

lo' - 8 -

6 - d

4 -

- . - 2 7 2 -

i o ' - E

b

a tric field intensification factor M due to geometric asperities on the

io0 -

5.0 E" W / m ) ' 3.0 4.0

Figure 13. Single electron emission rates SEERS vs. Ell2 according to Richardson-Sciottky for: (a), (b), (c), A1 with increasing oxide lay& thickness; (d), (e), (f), Nb with increasing oxide layer thickness. The M factor for A1 having a natural 2 to 3 nm oxide layer may

seem odd as it is less than unity, but it must be remembered that Equation (4) was found not to apply to our earlier [lo], higher than Equation (4) neglects the presence of an oxide layer. If this is taken

144 Guile et al.: High-field Single Electron Emission in Compressed Gases

E

14 16 18 20 22 24 25

oxide layer thickness

Al, 99.999% Nb N, E IN, E l & E l &

2-3 nm 50-60 nm 160 nm 2-3 nm 50-60 nm 200 nm 0.6 0.6 0.7 16.8 0.76 15.2 6.25 15.2 8.75 0.65 0.71 0.75 18 2.7 16.4 16 16 18.5 1.1 1.35 1.6 19.2 4.8 17.2 18 16.4 23 1.43 1.8 2.4 20 10 18.8 48.6 18.8 80 1.7 2.85 3.4 22.4 20 20.4 60 20.4 95 2.5 3.8 4.45 24.4 26 22 155 22.6 227 2.85 6.5 25.6 37 23.6 326 23 500

into account in a simplistic manner, then the M term in Equation (4) becomes M / E , where E, is the permittivity of the oxide layer. It is interesting that E, N 40 for NbzO5 and for A1203 E, - 10.

6. FINAL CONSIDERATION

The results reported in this paper, notably that hard cathodes emit electrons more freely under a high applied electric field, than soft cathodes and thus yield Paschen characteristics which lie below those for soft materials, flatly contradicts the data obtained by Trump, Cloud, Mann and Hanson [3], who found that, for instance, stain- less steel cathodes contribute to a 50% higher electric compressed gas strength than aluminum cathodes. Mitigating considerations for this difference are that Trump et al. [3] worked at voltages approaching 1 MV, gas pressures up to 250 MPa and inter-electrode gap distances reaching almost 2 cm. In contrast, our present work is limited to 20 kV, 0.5 mm respectively. There can be little doubt that the secondary ionization coefficient in its photo-electric form (ie. radiation &om excited gas molecules) which, in our measurements in compressed gas mixtures comprising ethane, was quenched (suppressed), plays a significant role in Trump et al. 1950 work, because, for instance, Llewellyn-Jones [22] has shown experimentally that A1 has a much larger secondary ionization coefficient, be it under the form of posi- tive ion bombardment, than mild steel.

7. CONCLUSION

1. A correlation has been established between the SEERS and the bulk modulus (hardness) of materials in that the larger the modulus, the higher the SEERS, for a given electric field. Analysis shows that this is due to the fact that, using the polishing method adopted, soft materials like aluminum can be given an almost ideal finish (electric field intensification factor M close to unity) whilst hard materials like niobium have a larger factor, M rv 7.

2. For a given cathode material and electric field, SEERS increase, surprisingly with increase in oxide thickness.

3. SEERS contribute to the sparking process in that materials with low bulk modulus have a higher Paschen characteristic and vice ver- sa; similarly the thicker the oxide layer, the lower the Paschen char- acteristic. This contribution is further substantiated by a gas pressure effect observed both with SEERS and Paschen characteristics.

4. With the present polishing procedure adopted, no spark condi- tioning was observed.

ACKNOWLEDGMENT Thanks are due to Mr. Brian Cox of the Central Electricity Research

Laboratory, Leatherhead for encouragement through the gift of the test vessel enclosure with bushing. The careful word processing of this paper by Mrs Ruth Baldwin is gratefully acknowledged.

REFERENCES [1] A. E. Guile, R. V. Latham and A. E.D. Heylen, "Similarities between

Electron Emission and Consequent Breakdown Processes in High- Pressure Gases and in Vacuum", IEE Proc. A, Vo1.133, pp. 280-284,1986.

[2] A. H. Cookson, "Review of High Voltage Gas Breakdown and Insulators in Compressed Gas", IEE Proc. A, Vol. 128, pp. 303-312,1981.

[3] J. G. Trump, R. W. Cloud, J. G. Mann and E. P. Hanson, "Influence of Electrodes on dc Breakdown in Gases at High Pressure", Electrical En- gineering, Vol. 65, pp. 961-964,1950.

[4] F. Llewellyn-Jones and E. T. De La Perrelle, "Field Emission of Electrons in Discharges", Proc. R. Soc. London Ser. A, Vol. 216, pp. 267-279,1953.

[5] F. Llewellyn-Jones and C. G. Morgan, "Surface Films and Field Emis- sions of Electrons", Proc. R. Soc. London Ser. A, Vol. 218, pp. 88-103, 1953.

[6] R. H. Fowler and L. Nordheim, "Electron Emission in Intense Electric Fields", Proc. R. Soc. London Ser. A, Vol. 119, pp. 173-181,1928.

[7] M. J. Morant, "Interpretation of Experiments on Electron Emission in Spark Gaps", Proc. Phys. Soc. B, Vol. 68, pp. 513-520,1955.

[8] L. Williams, D. Pulle, J. Sheard and A. E. D. Heylen, "Electronic System for Measuring Non-Destructively Single Electron Emission Rates from Surfaces in Compressed Gases Under High Electric Fields", Int. J. Elec-

[9] A. E. D. Heylen, A. H. Hitchcock and A. E. Guile, "A Novel Non- Destructive Method of Measuring Electron Field Emission", Proc. 5th Int. Cod. on Gas Discharges, IEE Conf. Publication No 165, pp. 308- 311,1978.

[lo] A. E. D. Heylen, A. E. Guile, and D. V. Morgan, "Electron Field Emission From Copper with Various Thicknesses of Oxide Film", IEE Proc. A, Vol.

[ l l] S. Kojimo and K. Kato, "Statistical Study of Electron Avalanches in Gaseous Discharge", J. Phys. Japan, Vol. 11, pp. 322-326,1956.

[12] A. H. Cookson, B. W. Ward and T. J. Lewis, "Townsends First Ionization Coefficient for Methane and Nitrogen", Br. J. Appl. Phys., Vol. 17, pp.

[13] R. A. Wysman, "Breakdown Probability of a Low Pressure Gas Dis-

[14] W. Legler, "Zur statistik der electronen lawinen", Z. Phys., Vol. 140, pp.

tronics, Vol. 66, pp. 289-309,1989.

131, (2), pp. 111-117,1984,

891-903.1966.

charge", Phys. Rev., Vol. 75, pp. 833-838,1949.

221-240,1955.

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 4 No. 1, February1997 145

[15] A. E. D. Heylen, “Ionization Coefficients and Sparking Voltages in Ar- gon and in Argon-Ethane Mixtures”, Brit. J. Appl. Phys. (J. Phys. D.),

[16] H. Raether, Electron avalanches and breakdown of gases, Butterworth, 1964.

[17] A. J. Muhammad, D. V. Morgan and A. E. Guile, “Electronic Conduction in Nb/Nb205/In Structures and the Effect of Space-Charge Overlap”, Phys. Stat. Sol., Vol. 90, pp. 371-38,1985.

[18] M. A. Salim, L. Williams, A. E. D. Heylen and A. E. Guile, ”High-field Electron Emission from Cathodes Having Various Thicknesses of Oxide Film”, Proc. 8th Int. Conf. on Gas Discharges and their Applications, Oxford, pp. 303-306.1985.

[19] R. V. Latham, HV vacuum insulation - the physical basis, Academic Press, London, 1981.

[20] R. Coates, ”Role of the Surface/Gas Interface in the High Field Electrical Breakdown of Gases”, Science Research Council Report, Swansea Uni- versity Phys. Dept., 1976.

[21] T. E. Stern, R. S. Gosling and R. H. Fowler, ”Further Studies in Emission of Electrons from Cold Metals”, Proc. R. Soc. London Ser A, Vol. 124,

[22] F. Llewellyn-Jones, Ionization and breakdown of gases, Methuen’s

[23] G. Dearnaley, ”A Theory of the Oxide-Coated Cathode, Thin Solid

Vol. 1, pp. 179-188,1968.

pp. 699-723,1929.

Monographs on Physical subjects. Figure 4,7. Methuen: London 1957.

Films”, Proc. R Soc. London ser A, Vol. 3,161-174,1969.

[24] A. E. Guile and A. E. D. Heylen, ”Magnetic Arc Movement from a Multi- collisional Viewpoint”, Proc. 6th Int. Conf. on Gas Discharges and these Applications, IEE Conf. Pub No. 189, Pt2, pp. 94-96.

[25] A. E. D. Heylen, “Electrical Breakdown and Ionization in Nitrogen- Ethane for Mixture at High Pressure”, Proc. 15th Int. Conf. on Phenom- ena in Ionized Gases, Minsk (USSR), PtII, pp. 607-608,1981.

[26] T. W. Dakin, ”Breakdown of gases in uniform fields. Paschen curves in N2 Air, SFs, H2, and He”, CIGRE Study Committee 15, Report 1977.

[27] T. J. Lewis, ”High Field Electron Emission from Irregular Cathode Sur- faces”, J. Appl. Phys., Vol. 26, pp. 1405-1410.

1281 I. W. McAllister and S. Vibholm, ”The Field Enhancement Factor of Sand-Blasted Electrodes”, Proc. IEEE Int. Symposium on Electrical In- sulation, Baltimore, pp. 307-309,1992.

[29] G. N. C. Kaye & T. H. Laby, ed. Longmans Physical & Chemical Con- stants 1992.

[30] K. A. Gschneider, ”Physical Properties and Interrelationships of Metal- lic and Semi-Metallic Elements”, Solid State Physics, Vol. 16, pp. 276- 426,1964.

Manuscript was received on 15February 1996, in final form YAugust 1996.