# Vacuum Breakdown and the Transition to the Vacuum Arc

As the voltage across a contact gap in vacuum is raised one or more of the pre-breakdown phenomena discussed in Section 1.3.3 will be observed. On continuing to increase the voltage, these various events can increase in intensity and eventually a breakdown of the vacuum gap will occur. If this happens with a vacuum interrupter in a power circuit, a vacuum arc will result which will permit the circuit current to flow until it is interrupted. Because the vacuum arc voltage is usually much lower than the circuit voltage, the circuit impedance will determine the magnitude of this current. It is important to note that the initiation of the vacuum breakdown process differs considerably from the Townsend avalanche breakdown in atmospheric air (or in other high-pressure gases) discussed in Section 1.2. In the gas breakdown, once a high enough field is impressed across the open contact gap, only one or a few initiating electrons are required to begin the electron avalanche in the gas. Once the avalanche has begun to develop, the transition to the arc is extremely rapid (< lps). If the current in the arc in air is greater than about 400 milli-amperes, the arc will be self-sustaining [127] and will develop a cathode root during the breakdown phase that is capable of supplying the electrons to maintain current continuity. During the avalanche process the development of a neutral plasma (for conducting the current) in the inter-contact region occurs as a direct result of the avalanche process where ions are produced as copiously as are the electrons. The electrons, ions and neutral atoms in this region are in local thermodynamic equilibrium [127]: i.e., their temperatures are approximately equal Te = Tj = Tn. In the vacuum breakdown case, it is necessary to first of all establish a cathode region that can supply a continuous supply of electrons. Second, it is also necessary to establish an ionization process that will supply enough ions to produce and maintain a quasi-neutral plasma in the contact gap. If these two conditions are not met, then the full breakdown of the contact gap in vacuum will not occur. Instead, a microdischarge will be observed which will soon self-extinguish and the current will cease to pass between the contacts.

Each of the pre-breakdown phenomena discussed above has influence on the vacuum breakdown. Shioiri et al. [128], using voltage pulses, observe that lc can increase to greater than 20mA as the voltage increases without the contact gap breaking down and then can drop to a low value as the voltage pulse decreases to zero. They show that this current increase and decrease follows the Fowler-Nordheim equation and that a value of /3 can be determined for each voltage pulse. In their experiments when Ie increases to about 30mA vacuum breakdown takes place. These authors also show that the absorbed power at breakdown (i.e., PB = UR x IB) is approximately constant for smooth Cu spheres (~ 5000W) with contact gaps in the range 2mm to 4mm. From Figure 1.55 it can be seen that for an I„ = 30mA, the subsurface anode material could have reached the boiling temperature in less than 5ps. Visual measurements of the contact gap using high-speed cameras show light first from the cathode and then much stronger and more dispersed light from the anode [129, 130]. The macroscopic field at breakdown is Eg ~ 4 - 8 x 107 Vrrr‘ [54]. For Cu-Cr contacts with/3 = 100 - 300, the microscopic field for breakdown is Em ~ 8 x 109 - 11 x 109 Vnr1 [61, 131]. The thermal stability and mechanical properties of the anode also influence the breakdown voltage. Anodes with low thermal conductivity and low vapor pressure for a given temperature tend to have lower values of UB [99, 132]. Anodes with high tensile strength (note: tensile strength » ^(hardness)]) have higher values of UB [54, 83]. Zhou et al. [133] show in Figure 1.68 an example of the voltage breakdown in vacuum between a needle cathode and a plane anode.. Flere a very fast-rising voltage pulse (> 70ns) shows a breakdown initiating at tBD. In this case the breakdown results entirely from field emission

FIGURE 1.68 A streak image for the initial stage of a vacuum breakdown process: cathode material W, anode material Cu, gap length 5mm, for a very fast voltage rate of rise to breakdown (~ 70ns) for a total voltage pulse width of 5 (is and the steady state arc current 80 A (Courtesy Zhenxing Wang).

FIGURE 1.69 The effect on the vacuum breakdown voltage of introducing particles on to polished contacts as a function of particle diameter [101].

electrons from the cathode. The anode flare is only initiated about 0.4/rs later at tFB. This indicates that for a very fast-rising voltage pulse, the anode sub-surface heating is delayed.

Particles can certainly influence the breakdown voltage for a given contact gap. Kamikawaji et al. [101], for example, show the effect that different diameter particles have on reducing the breakdown strength of a carefully prepared, polished vacuum contact system; see Figure 1.69. It is interesting to note that the smallest particles lower UB the most. Figure 1.70 shows another data set taken by

FIGURE 1.70 Effect of the introduction of microparticles on the vacuum breakdown voltage for Cu-Cr contacts with a rough finish and for Cu contacts with a mirror finish [134].

FIGURE 1.71 Average breakdown voltage between machined Cu-Cr contacts for clean contacts and after the introduction of 7 ,wn and 80 /.ял microparticles onto the contact surface [134].

Sato et al. [134] for clean, polished Cu contacts and for Cu-Cr contacts with a practical roughness expected in a manufactured vacuum interrupter. The influence of microparticles on the UB value for a rough surface is much less than that on a polished surface. The dependence of UB as a function of the spacing between the rough-finish, Cu-Cr contacts for two particle sizes is shown in Figure 1.71. These data are of great importance to a vacuum interrupter designer who has little control over the microscopic roughness of the contact surfaces during the vacuum interrupter’s operating life. These data suggest that the effect of particles on a rough surface is minimized by the roughness. So, if the vacuum interrupter designer takes into account an initial contact surface roughness, then it is possible for the contact structure to maintain its high voltage performance in spite of particles being produced each time the vacuum interrupter switches current. Microparticles for the most part travel from anode to cathode [135]. Indeed for a slowly rising voltage, anode material is usually present on the cathode after vacuum breakdown [95].

One compelling argument for particle initiation of vacuum breakdown is Cranberg’s analysis [136]. He has proposed that once a microparticle obtains a critical energy Wc from the electric field, the impact of this particle on a contact surface would result in the vacuum breakdown of the contact gap. Thus from Equation 1.60, the impact energy per unit area from a particle of radius r can be approximated by:

Thus:

where Kc is a constant. Further refinement of the exponent for the contact gap d for the case of a dc voltage has it ranging from 0.5 to 0.625 [137]. Experimental measurements by Sato et al. [134] show even greater variations in the exponent, from 0.3 to 1.1, as is also seen in Figure 1.20. They also show that the exponent has a strong dependence upon particle size and contact gap. Farrall [138] has shown that for fast impulse voltages a single transit particle could result in breakdown voltage UB « rl/sdm for and a breakdown voltage UB r‘/3d5/2 for pulses with a constant rise time. The fact that UB a dand that a relationship of this nature can be explained by a microparticles effect has given rise to an acceptance that microparticles do play an important role in vacuum breakdown especially in contact gaps greater than a few millimeters, i.e., the range of contact gap common in vacuum interrupters. However, the exact details of how a microparticle initiates a sustainable vacuum arc are not usually discussed. While microparticles impacting the cathode can initiate a local discharge at the cathode, the development of a sustained vacuum arc still needs to be researched. The experiments by Ejiri et al. [110-112] show that the discharge between a microparticle and a cathode does not necessarily result in the breakdown of the whole vacuum gap. By introducing microparticles onto a planar contact they observe their transit between the open contacts under an impressed ac voltage. Figure 1.60 shows examples of discharges that can occur between a microparticle and the cathode contact. There is no breakdown of the full vacuum gap in these examples. From the discussion in Section 1.3.3, however, it is possible that microparticles can exhibit a number of effects:

• 1. Direct impact on the contact surface after one transit across the contact gap
• 2. Impact on the contact surface after a number of gap transits especially w'ith an ac voltage
• 3. The effect of the impact depends upon the particle size, the impact velocity and the potential drop across the contact gap
• 4. A particle as it gets close to one or other of the contacts may initiate a high local field and this can result in enhanced field emission currents and even a local discharge
• 5. The particle may be evaporated during transit by the electrons emitted from the cathode

Finally, as we have already discussed in Section 1.3.3, microdischarges can also have an influence on the breakdown of a vacuum gap. Their occurrence, however, does not usually result in a vacuum breakdown. It is only when the charge passed exceeds a certain value will a microdischarge enhance the opportunity for a vacuum breakdown to occur. As stated above, the breakdown of a vacuum gap will only proceed to a conducting vacuum arc if:

• 1. The cathode region develops into an efficient source of electrons
• 2. There is sufficient gas for the electrons to ionize
• 3. A region for the long-term production of ions is established

Let us first of all consider the effects of the electron emission from a cathode micro-projection. As we have already shown in Figure 1.36(b), the current lc from this cathode region increases exponentially as the voltage across the vacuum gap is increased. At very low values of Ie the temperature of the projection will slowly increase. When the current density je reaches a value of about 2 x 1012 Anr2, Fursey [139] has shown, with a two-dimensional analysis of a long projection whose tip radius is 0.4yum, the very rapid growth in temperature shown in Figure 1.72. In performing this analysis, Fursey considers two major energy sources into the microprojection. First, the current flow through the bulk of the metal produces the usual Joule heating effect and, second, it can initiate the Nottingham effect. [56, 140, 141]. The Nottingham effect results from the fact that the average energy of an emitted electron will be different from the average energy supplied by its replacement electron from the metal lattice inside the projection. For low temperature field emission, electrons will be emitted from states below the Fermi level, so there will be a heating effect. At high temperatures the electrons will tunnel from populated states above the Fermi level and so will give rise to a cooling effect. The transition between heating and cooling depends upon

FIGURE 1.72 A numerical calculation of the effect of microprojection heating by a high density, field emission current (jFE = 2xl012 A/m2); (a) the temperature as a function of time: Curve-1, the microprojection’s surface temperature and Curve-2, the maximum temperature below the microprojection’s surface and (b) the temperature distribution along the microprojection’s axis (note, the “0” on the abscissa is at the microprojection’s tip and the distance is in /rms below the tip into the microprojection) [139].

FIGURE 1.73 A cross-section of an electron emitting microprojection on the cathode used to develop Figure 1.72 [139].

the metal’s work function and the microscopic electric field at the microprojection; a typical value is approximately 1500 C. As the electron density in the projection increases and the projection increases in temperature, it is important to note that the highest temperature is not at the surface of the projection, but inside it; see for example, Figure 1.73. Other calculations show that at high current densities, the electron temperature exceeds the phonon temperature in the metal lattice. This difference can be very significant at current densities greater than 5xl012 Airr2. In fact, at these current densities the microprojection will be destroyed in ~ 3ns [139]. Is it possible to achieve these current densities in a cathode microprojection? Let us take the information given in Figures 1.36(a) and (b). If we extrapolate the data in Figure 1.36(b) for Ie to the breakdown voltage of 50 kV for this system, then Ie = 11.1mA. Thus, with Ae = 4.8 x 10-16 m2, the current density at the cathode in this experiment would have been:

which is of the same order of magnitude as used in Fursey’s calculation.

As discussed previously, the initial emission current results from field emission at the cathode projection and the current density je is given by Equation (1.48). Once larger currents begin to flow the effect of electron space charge would limit the maximum current density jc by Child’s law [142].

where /„ is the current at the anode, S is the surface area at the anode receiving current, e0 is the permittivity in free space, q is the electron charge, me its mass, U voltage across the contact gap d. In a normal contact gap, which has large parallel disc contacts, the expected roughness of the contact surface would be small with respect to the contact separation d. The effects of space charge

FIGURE 1.74 Schematic graph showing how the slope of a Fowler-Nordheim plot can be modified by space charge effects and by emission enhancement effects.

limitation can be observed in the Fowler-Nordheim plot as is illustrated in Figure 1.74. As can be seen in this figure, if the line drops below the linear line, then the emission current is space charge limited. As we have already discussed the electrons from the cathode microprojection would remain in a narrow cone on their transit to the anode. The space charge would be expected to reduce the effective field at the emission site and hence limit the field emission current [143]. Fursey’s compelling model of the cathode micro-projection’s increase in temperature requires a current density in the range je = 1012 - 10B A.nr2. When this current density is reached there is a violent rupture of the cathode micro-projection, because surfaces forces holding it together can no longer do so. Before this current density can be reached by pure field emission, Dyke et al. [144-147] have shown that it would be space charge limited. Thus, the electric field near the emitting site would also decrease once the current becomes space charge limited. This in turn would lower je and the temperature of the emitting site.

How then is it possible to continue increasingyf? One answer results from the interaction of the emitted electrons and the adsorbed gas on the cathode’s surface which Aoki et al. [124] demonstrate exists even at a vacuum pressure as low as 10~6Pa. A proposal by Schwirzke et al. [148] is illustrated in Figure 1.75. They suggest that the increase of je to a value greater than the space charge limited value requires the presence of ions at the cathode-emitting site. In their model adsorbed gas at the cathode-emitting site is desorbed by the joule heating of the site. This could release a monolayer of 2 x 1019 molecules.m-2 and an expanding gas cloud would appear across the cathode. For a typical vacuum interrupter contact gap, the breakdown voltage is greater than the BIL value, so for an 8mm

FIGURE 1.75 The ionization of desorbed monolayer at the cathode reduces space charge limitations on electron emission from a cathode microprojection [148].

gap UB may be lOOkV. Thus, emitted electrons will have energies of less than lOOeV at less than Spin from the contact surface. Figure 1.6 indicates that electrons with this energy will ionize this gas efficiently. The resulting ions would return to the cathode. The heating of the projection would then involve the field emission current plus the returning ion current. The total current density je in the projection would be:

The returning ion bombardment not only allows a rapid increase of je, but also could lead to further gas desorption and could even result in initiating an evaporation of the cathode metal. As more ions are produced, the electric field at the cathode will be enhanced,^ will increase and the microprojection will quickly become unstable and explode. The subsequent release of metal vapor above the cathode provides a medium for the production of metal ions and a plasma flare will develop in the region of the cathode’s microprojection. This cathode flare would then expand toward the anode. Uimanov [149] has developed a model that shows the space charge may not be the limiting factor for the emitted electrons close to the surface of a cathode microprojection. For emitters with a tip radius less than lOOnm the Fowler-Nordheim current density can reach about 1010 A.cnr2 for applied voltages 250-300kV. In Figure 136a, the emitter area is 4.8 x 10~12 cm2. In this example the emission current can reach 4.8 x К)-2 A or 48 mA. This current is well above the value of 11.1 mA calculated from Figure 136b at the breakdown voltage of 50 kV.

Another source of ions could be the anode. As I have discussed in Section 1.3.3.2, the field emission current penetrates the anode. It heats a well-defined volume below the anode’s surface. When this volume reaches a temperature close to the metal’s boiling point a vapor flare will erupt into the inter-contact gap. At this temperature thermal radiation from the anode flare will emit an

FIGURE 1.76 The approximate expansion of the anode flare volume from a Cu-Cr(30wt.%) across a 2mm contact gap calculated from figure 4 in reference [151].

intense white light generated by the thermal motion of the metal atoms. The initial volume of the anode at the anode’s surface will have a very high density. At this stage there could be a small, but finite probability that even high energy electrons from the cathode flare may achieve some degree of ionization. As the anode flare expands its density will rapidly decrease. As discussed in Section 1.2.1, Figure 1.6, it seems unlikely that this lower density metal vapor would be ionized directly by the electrons with energies greater than 10s keV passing through it. Indeed, Nagai et al. [150, 151] observe the spectra from an anode flare from Cu-Cr(35wt.%) contacts as it expands across a 2mm contact gap in vacuum. They find that the ion densities near the anode are higher at 100ns after the flare’s initiation than at 200ns. Also, the ratio of Cu to Cr atoms in the anode flare is similar to that in the contact material. Figure 1.76 shows the approximate expansion of the anode flare from their experiment. Bochkarev et al. [152] also observe the spectra during the breakdown of the vacuum gap between a Cu rod cathode and a Mo planar anode. They conclude that the anode flare shows mainly neutral metal spectral lines while the cathode flare shows strong spectral lines from singly and doubly ionized Cu atoms. Another possible, but unlikely, source of ions could result from the model adopted by Davies et al. [93, 94] in which the electron beam w'ould evaporate a particle pulled from the anode and the region behind the particle would be ionized by lower energy electrons emitted from the particle itself, Figure 1.49. The ions produced by this process would then travel to the cathode and alleviate the space charge limiting effects. These metal ions would then also enhance je and give rise to the instability of the cathode-emitting site.

If the line in Figure 1.74 is above the Fowler-Nordheim linear line at high current densities, then two effects can be occurring. First of all, ions returning to the cathode will reduce the space charge limitation and even enhance /e. Second, as the cathode projection reaches a higher temperature, its metal will soften. Emelyanov et al. [153] show that this can result in the local electric field pulling the projection into a finer point; hence increasing ()m and Em. Some experiments even suggest that the tip of the cathode projection is in the liquid phase just before the explosive rupture of the electron emitting microprojection [154]. Mesyats et al. [155] have developed the idea that the ultra-high field at a microprojection will result in a decrease in the metal’s potential barrier

FIGURE 1.77 Multiple cathode flares during the initial stages of vacuum breakdown between a Cu- Cr(30wt.%) anode and a Cu cathode [150, 151].

FIGURE 1.78 The position of metal vapor from the cathode and anode contacts after the initial observation of emission current with a slowly increasing dc voltage across the contacts as a function of time and contact gap position [95]; anode material 0 and cathode material □

below' its w'ork function. This can result in a substantial increase in the electron density near the emitter’s surface. They show' that if this effect does occur, saturation of the field emission current does not happen and the current density increases more or less linearly with the increase with the electric field. Once the je exceeds 10l2 to 1013 A.nr, the projection w'ill explode and it w'ould be possible to form a plasma in the dense metal vapor cloud. Interestingly enough this can occur at the same time at more than one site [77, 154]. Figure 1.77 shows an example of multiple cathode flares [150, 151].

In an interesting series of experiments, Davies et al. [94] have explored the origin of metal vapor during the breakdown phase in the intercontact gap using a slowdy increasing dc voltage across it. To do this they use different metals on the cathode and the anode. In one experiment, Figure 1.78, they use a Cr cathode and a Cu anode and in a second experiment they used a Cu cathode and a Cr anode. They make observations of the presence of metal vapor as a function of time in three positions: close to the cathode, close to the anode and at mid-gap. They show that in all cases the first observable metal vapor comes from the anode. This observation is consistent with the expected heating of the anode’s subsurface by a slowly increasing emission current as the voltage across the contact gap increases. Figure 1.55 shows that the interior of a Cu anode can reach the boiling point at a current of 1mA in a few' micro-seconds. Metal vapor from the cathode, however, is detected close to the cathode w'ithin 5 to 10 ns after the initial detection of emission current. In a subsequent series of experiments [156] using a rectangularshaped, pulsed voltage source, they recorded whether anode material or cathode material is observed first as a function of breakdown delay time tB, see Figure 1.79. Here tB is clearly shown as a function of impressed voltage. In each case the cathode material is observed first if the tB is

FIGURE 1.79 Breakdown delay times as a function of breakdown voltage for a rectangular pulse applied to the open contacts; (a) Cu cathode-Cr anode and (b) Cr cathode-Cu anode; ■ breakdown events in which radiation from anode vapor is emitted first and □ breakdown events where radiation from cathode vapor is emitted first [156].

less than or equal to 10 psec. Anode material is only observed first for longer breakdown times. The inferences from these studies are: (a) although the hypothesis presented by Davies et al. [93, 94] of a particle being pulled from the anode’s surface which then gives rise to a plasma cloud is intriguing, a more likely explanation of their experimental results is that they observed an anode flare that resulted from the emitted electrons heating the subsurface of the anode; and (b) cathode processes can occur extremely rapidly and (c) the anode processes take more time to develop. Certainly, Figure 1.68 shows that for a rapidly rising voltage pulse the cathode flare is initiated well before the anode flare. For a slowly applied dc voltage across a 1mm contact gap [156]: 1 2 [1] [2]

FIGURE 1.80 BIL and ac vacuum breakdown voltage as a function of contact gap [91].

3) As the voltage U across the contacts increases the power input to the cathode goes as jf, but the power input to the anode goes as je x U

and for a fast-rectangular voltage pulse across a 1mm contact gap [156]:

• 1) je2 x hi = constant (for times Ins < tH < 4ps)
• 2) If k* = applied field/ dc breakdown field (к* < 1.2 for tB > JO /js. And к *> 1.3 for tB < JO ns)
• 3) For tB = 160 fjs anode material is always seen first; and for tB = 14 /usee cathode material is always seen first.

These observations will have an impact on vacuum interrupter design. As I have discussed in Section

1.1 the design has to satisfy a wide range of impressed voltages and shapes across the open contact gap; from the BIL impulse voltage to the ac withstand voltage. Fortunately, experiments have shown, Figure 1.80 [91], that a vacuum gap can withstand a higher BIL pulse than it can a 50 Hz ac voltage. Here UB for the ac voltage is about 0.7 UB for the BIL voltage pulse. This indicates that for these contact gaps, breakdown processes with times greater than 5 Ops play a role in their eventual vacuum breakdown. Thus, if the internal design of a vacuum interrupter satisfies the BIL requirements given in Table 1.1, it will also pass the ac withstand test, but not vice versa. I discuss this further in Section 1.4.2. While this is true for the internal design of the vacuum interrupter, it is not necessarily valid for the external dielectric design. So, when developing a new vacuum interrupter design, the internal and external high voltage withstand capabilities must be considered separately.

Another example of an experiment to show the spatial distribution of light from a contact gap in vacuum during the breakdown process is shown in Figure 1.81 [129]. The original streak photograph clearly shows an initial intermittent light from the cathode, which only becomes steady once light from the anode appears. This observation is similar to that shown in Figure 1.68 for a very fast rising voltage pulse across the open contact gap. Other photographic observations of the vacuum gap show simultaneous radiation from the cathode and from the anode [77, 129, 150, 151, 153, 157]. In general, the thermal radiation from the anode tends to be more intense than that from the cathode. This has led some researchers to conclude that the anode plays the dominant role in establishing the vacuum arc. While the anode region can initially develop some ions [151], it is

FIGURE 1.81 The pre-breakdown, spatial distribution of light in a contact gap showing light first from the cathode [129].

the development of an electron emitting cathode spot that determines whether or not a sustained vacuum arc is formed. One problem with the photographic observation of the cathode is that the cathode spot’s initial formation is very small [126, 151, 153]. The high-pressure plasma that forms directly above it moves away at very high speeds. Thus, its density decreases rapidly and the radiation from it is undetectable at distances of about 0.1mm. The thermal radiation from the anode flare, on the other hand, can have a much broader luminous volume, which can overwhelm the detection of radiation from the cathode; see for example, Figure 1.77.

• [1] At mid gap the anode material is seen before cathode material
• [2] Radiation is seen initially in the cathode region