Effect of breakdown path on discharge of Micro - gap electrode

In order to study the causes and in�uencing factors of the "plateau period" of breakdown voltage curve at the micron scale, three groups of different electrodes were set up for gas discharge experiments within the range of 20-100 𝜇 m electrode spacing and 1-100kPa air pressure, and the results were analyzed. Under the conditions of different electrode curvature radii, the breakdown voltage curve deviates from Paschen curve with the change of air pressure, and there is a "plateau period". The "plateau period" is the (Pd) min when the charged particles meet the minimum breakdown voltage by changing the path near the electrode edge, and the "plateau period" range is affected by the radius of curvature of the electrode edge. However, the breakdown voltage curve of the electrode edge after insulation treatment is consistent with the Paschen curve, and the breakdown path is not along the minimum spacing between the electrodes at the micron spacing.


Introduction
Micro-discharge usually refers to the gas breakdown phenomenon when the gap distance is submillimeter or smaller [1]. Micro-spacing discharge has application prospects in many elds, such as biomedicine and micro-driven motor system [2][3][4]. The breakdown characteristics of micro-spacing gas discharge are different from that of conventional discharge.
Researchers usually use Paschen's law (U b =f (Pd)) to predict and calculate the breakdown voltage. The breakdown voltage U b is a function of the product of pressure P and spacing d. Different Pd values correspond to different breakdown voltage values [5][6][7][8]. British physicist Thomson pointed out in his book "Current in Gas" that Paschen's law is only a special case of the more general principle of discharge similarity in a uniform electric eld, which means that Paschen's law is limited [9]. However, in the experiment, it was found that after the breakdown voltage reached the minimum value, change the Pd value, and the breakdown voltage will remain at the minimum value for a distance, which is called "transition zone" or "platform period". In this regard, scholars at home and abroad have carried out research and exploration, and achieved some results. Wang Xinxin and other scholars analyzed the separation and crossover phenomenon of Paschen curve through numerical simulation. For the non-uniform electric eld in the air gap of the at plate, the breakdown voltage U b is not only a function of the combined variable Pd, but also affected by the ratio of the electrode spacing d and the electrode radius r, that is, Ub = f (Pd, d/r), which supplements Paschen's law [10]. Wang Ronggang and other scholars used particle method (PIC/MCC) to simulate and analyze the initiation and development process of electrode breakdown discharge under the pin-plate electrode structure. It is found that under the same air pressure, the diameter of the electrode discharge circuit with different spacing is also different. In a small air gap, the self-modulation effect of the electron makes the discharge path longer [11], making the PD value approximately equal to the Pd value corresponding to the minimum breakdown voltage, that is, PD ≈ (Pd) min (D is the actual breakdown path distance). By establishing a DCP model of two non-parallel straight plate electrodes, Yu Bo and other scholars found that when the pressure changes, the initial path of breakdown will shift [12], and the entire electrode channel will always choose the path most likely to cause breakdown under different working conditions. At present, based on the breakdown characteristics of the at electrode with micron spacing and the appearance of the breakdown voltage "plateau period", Paschen curve is no longer fully applicable to the breakdown characteristics of the at electrode. In order to verify the cause of "plateau phase" in the discharging phenomenon of plate-plate electrodes with micro-spacing and the in uence of the edge of electrodes on the discharging rule. This paper establishes a micro-spacing discharge experimental platform, compares the discharge experimental phenomena of brass electrodes under three different edge conditions, and studies the impact of the breakdown path of the at electrodes on the discharge by changing the air pressure. First, the experimental platform is set up. Figure 1 is the schematic diagram of this experimental platform, which mainly includes plasma power supply, oscilloscope, pressure regulator, vacuum pumping device, experimental chamber and measurement device.

Experimental measurement method
In this experiment, brass was used as the electrode material with a diameter of 3 mm. The roughness of the surface of the electrodes has a great in uence on the breakdown voltage. The surface of the electrodes is polished with 5000 mesh sandpaper, and cleaned with deionized water. The processed electrodes were then examined and recorded using a scanning electron microscope (SEM).
After the experimental platform is set up, the speci c experimental operations are as follows: First, add a low voltage (about 10V) to the electrodes, control the distance between electrodes by controlling the displacement platform, and observe the oscilloscope. When the measured current and voltage increase suddenly, the electrodes are in contact with short circuit, which is the zero point of the electrodes. Adjust the distance between electrodes to the distance required by the experiment, close the vacuum chamber after xing the electrodes, and control the air pressure in the vacuum chamber through the pumping device. When the pressure is stabilized, a voltage is applied, and the voltage is slowly and uniformly increased by the voltage regulator. At the same time, the oscilloscope is observed. When the voltage and current waveforms in the oscilloscope change abruptly, they are regarded as breakdown and experimental data are recorded. To reduce the experimental error, experiments at each interval are repeated ve times, and the average voltage is taken as the nal value.
The air in this experiment is air, and the ambient temperature is about 25 ℃. There are three groups of comparative experiments. The curvature radii of the electrodes used in the experiment are 20 m and 100 m, respectively, and the edges of the electrodes are covered with insulating paint (in which the thickness of the insulating coating is greater than 40 m). Three groups of experiments were conducted at four different intervals to change Pd values by adjusting the air pressure and record data.

Experimental Results And Analysis
Based on the experimental platform, the breakdown voltage of brass electrodes at different pressures with the spacing of 20-100 m was measured using the spiral displacement platform and the vacuum chamber pressure regulator. The breakdown voltage U of brass electrodes with the product of P (gas pressure) and P and D (electrode spacing) as shown in Fig. 2  To analyze the trend of breakdown voltage during the change of air pressure, the curve of breakdown voltage with air pressure at xed spacing is shown in Fig. 2

Case2 data analysis
After insulating the edges of the electrodes, the experimental results are shown in Fig. 3. The relationship between breakdown voltage and Pd is shown in Fig. 3(a). The left end of the curves does not appear to be dispersed. The trend of breakdown voltage with Pd value is in accordance with Paschen curve. Paschen curve can be used to explain this kind of discharge. There was no obvious plateau period during the experiment. The breakdown voltage decreased rst and then increased with the increase of air pressure.
The breakdown voltage reached the lowest point after reaching the corresponding air pressure value, and the Pd product was around 60kPa·cm.

Case3 data analytics
The radius of curvature at the edge of the electrodes in Case3 is 100 m. The relationship between the breakdown voltage and Pd is shown in Fig. 4 (a). The curves corresponding to the different spacing are still segregated from Paschen curves at the left, and the segregation of curves is more severe than that in Case1. The breakdown voltage corresponding to the same Pd value at different spacing is also different. The trend of breakdown voltage with pressure at different spacing in Case3 is shown in Fig. 4 (b). Compared with Case1, it is obvious that the "platform period" range of breakdown voltage under each spacing group is enlarged signi cantly, the starting pressure is about 3 kPa, and the ending position corresponds to the corresponding Pd value of 60 kPa.cm for each spacing group. Both Case1 and Case3 have "platform phases", but the corresponding ranges are different.

Causes of the plateau
Thomson's theory shows that by applying an external voltage, free electrons distributed near the cathode are driven by an external electric eld, migrate from the cathode to the anode, and collide with ionized neutral gas molecules. Positive ions move to the cathode step by step, and generate secondary electron emission by impacting the cathode, which eventually breaks down. Quantitative calculations of an electronic avalanche, such as Eq. (1), show that collision ionization is related to the number of collisions (spacing multiplied by Pd of air pressure) and the average energy of electrons obtained during electron movement.
From the point of view of the average energy of electrons, the average energy of electrons affects the collision, adsorption, excitation and ionization of particles in the gas [13] . The reduced eld strength is an important reference. The average energy of electrons increases with the increase of the reduced eld strength. The expression of the reduced eld strength can be expressed as E/n or E/P. Where n is the concentration of gas particles and P is the pressure. From the point of view of collision ionization, the number of collisions of collision ionization is related to the collision ionization coe cient a (the product of the ionization coe cient a and the travel distance is the collision number).
Lower air pressure results in an increase in the average free distance of the electrons, and the number of collisions of particles in the unit travel decreases, which reduces the probability of collision ionization and makes it di cult to break down. With a xed spacing d, the air pressure decreases from the atmospheric pressure, and the breakdown voltage decreases rst and then increases. There is a pressure value P1 between them, which minimizes the breakdown voltage at this distance D. However, the "plateau phase" indicates that the breakdown voltage remains at the lowest point within a range of atmospheric pressure lower than P1. The collision ionization coe cient decreases when the air pressure is lowered, resulting in insu cient collision ionization times at the original spacing D. At this time, the breakdown path is no longer the minimum distance between the plates and is affected by the edge effect of the electrodes. The longer breakdown path increases the number of collisions to reach the most effective E/n, E/p or (Pd min ) condition at the minimum breakdown voltage of V min , so the breakdown voltage remains at the minimum point.

Simulation and Analysis of Field Strength Distribution of Electrodes
The edge effect of the electric eld distorts the electric eld at the edge of the electrodes, creating an uneven electric eld at the edge of the electrodes, and breakdown occurs when electrons travel a longer path. The eld strength of electrodes with different spacing and 330V voltage was simulated by software Maxwell. Figure 5 is a simulation of the eld strength distribution with a 20-um and 60-um electrode spacing, and Fig. 5 (a) and (b) are eld strength simulations with a curvature radius of 20 and 100 m, respectively.
(1) Case1 and Case3 eld strength distribution simulation comparison It can be seen that the origin is the center of the electrodes, the electric eld within the radius is uniform, and the intensity of the electric eld can be regarded as a constant value (E = U/d). The obvious electric eld distortion can be seen at the edge of the electrodes, and the in uence of the edge of the electrodes on the uniformity of the electric eld varies with the spacing. By comparison, it is obvious that a larger radius of curvature has a wider in uence on the electric eld distortion and a more serious degree of distortion. In micron spacing discharge experiments, the electric eld distortion caused by the edge of the electrodes has a great impact. The breakdown can be caused by the eld strength condition at the edge of the electrodes under certain conditions, which is the main reason for the "platform period".
(2) Simulation diagram of Case2 electrode eld strength distribution Under the same conditions, the eld strength simulation of the electrodes in Experiment Case 2 is carried out by software Maxwell, as shown in Fig. 6.
It can be seen that the electric eld is uniform within the radius centered on the origin of the electrodes. Direct current is applied in the experiment, so air cannot cause breakdown between dielectric without considering dielectric barrier discharge. Under Case2 experimental conditions, the electric eld generated by the charged electrodes can be seen as a strictly uniform electric eld, and the discharging rule conforms to the Paschen curve. When the optimal Pd value is reached to the minimum breakdown voltage and the pressure is continuously lowered or raised, the breakdown voltage will increase. At lower pressure, electrons cannot be maintained between electrodes by enlarging their own walking paths (Pd min ), that is, they cannot form a "platform period" [14][15][16].

The phenomenon and analysis of the electrode glow discharge
In terms of micro-breakdown paths, it is emphasized that the breakdown paths in micro-spacing are not the shortest distance between electrodes. For the comparison of breakdown paths, this paper has the following ideas: First, by observing the discharge phenomena of electrodes at different pressures during the plateau period; Second, an insulating coating is added to the edge of the electrodes. The discharging experiments were carried out with the electrode spacing xed at 60 m, and the experimental phenomena were compared. The left side is the anode and the right side is the cathode, as shown in Fig. 7. Figure 7 (a) is an electrode discharge at atmospheric pressure at which the breakdown voltage is about 750V and occurs in the middle of the plate. Then reduce the air pressure, the breakdown voltage reaches the lowest point of about 330V at 10kPa, and the discharge is dispersed in the middle of the electrode, as shown in Fig. 7 (b); Keep the voltage of 330V unchanged, reduce the air pressure to 7kPa, and the dispersion range is signi cantly expanded. The discharge phenomenon is shown in Fig. 7 (c); Continue to reduce the air pressure to below 5kPa, and the breakdown will not occur. Figure 8 shows the electrode discharge phenomenon with the electrode edge covered with insulating layer and the spacing of 60 m.
When the air pressure in the vacuum chamber is controlled at 10kPa, its breakdown voltage is about 330V. With the decrease of air pressure, the breakdown voltage will no longer remain unchanged, but will increase with the decrease of air pressure. At 7kPa, the breakdown voltage will increase to about 360V. The discharge phenomenon under different air pressures is similar, as shown in Fig. 8. The discharge range does not expand signi cantly with the decrease of air pressure, and its discharge law conforms to Paschen curve.
Based on the established experimental platform, the measured gas pressure range is 1-100kPa, the electrode spacing range is 20-100 m, and the discharge characteristics of the breakdown voltage of different electrodes are analyzed. The reason why the breakdown voltage of micro-spacing deviates from Paschen curve and the "plateau period" occurs is analyzed emphatically, and the following conclusions are drawn.
According to the analysis of three groups of experiments, the appearance of "plateau period" in the plateplate electrode is the electric eld distortion caused by the electrode edge effect, which forms an uneven electric eld. To ensure that the most effective Pd value is met at the minimum breakdown voltage, the appearance of "plateau period" is caused by the breakdown of particles through a longer path.
By comparing the experimental results, in the plate-plate electrode discharge experiment, the size of the curvature radius of the electrode edge will affect the modulation range of the particle breakdown path, that is, the range of the breakdown voltage "plateau period".
The "plateau period" is caused by the long path of particles when they break down between electrodes.
The scope of the "plateau period" indicates that the path extension when particles break down cannot be in nite. After the critical point is exceeded, the breakdown voltage will rise and the "plateau period" will be broken. Case1 experimental data curve Figure 3