Investigation of the discharge delay time in ionic crystals at the transition boundary of the discharge mechanism
Abstract Generated abstract
Discharge delay times in NaCl ionic crystals are examined near the critical thickness at which breakdown is expected to change from a single-avalanche streamer mechanism to a multi-avalanche streamer mechanism. Using liquid-electrode samples about 30 micrometers thick and rectangular high-voltage pulses with submicrosecond and nanosecond fronts, the study measures breakdown timing statistically at several overvoltages. At 5 percent overvoltage, the multi-avalanche mechanism gives a delay time of about 3.4 microseconds, while breakdown attributed to the single-avalanche mechanism occurs within the pulse front, less than 5 nanoseconds. The results show an abrupt difference of several orders of magnitude in discharge development time near the transition boundary, and indicate that increasing overvoltage increases the probability of fast, front-edge breakdown.
Full Text
STUDY OF THE DISCHARGE DELAY TIME IN IONIC CRYSTALS AT THE BOUNDARY OF A CHANGE IN THE DISCHARGE MECHANISM
L. G. NEKRASOVA
(Presented by the scientific seminar of the Research Institute of High Voltage)
At the Tomsk Polytechnic Institute, the mechanism of discharge development in solid dielectrics has been studied for a long time. On the basis of the investigations carried out, two schemes of discharge development in a “thick” and a “thin” layer have been developed [1].
The number of electrons in an avalanche is
\[ n_{\mathrm{e}} = 2\frac{d}{\lambda_{\mathrm{i}}}, \]
where \(d\) is the thickness of the dielectric,
\(\lambda_{\mathrm{i}}\) is the path length between ionizing collisions.
For sufficiently large \(d\), the amount of space charge at the anode from one avalanche is sufficient to initiate a streamer leading to breakdown. Breakdown is effected by a single electron avalanche; such a mechanism has been called the avalanche-streamer mechanism.
In a “thin” layer, the amount of space charge at the anode after the arrival of one avalanche may fail to reach the critical value necessary for streamer development.
In this case, breakdown occurs only after several electron avalanches arrive in a small region at the anode, creating a positive space charge at the anode that leads to the formation of a streamer. Such a discharge mechanism has been called the multi-avalanche-streamer mechanism. Its development requires a certain time—the time of accumulation of space charge—which determines the breakdown delay time, and in a thin dielectric layer it may be considerable.
On the basis of a study of the discharge development time in alkali-halide compounds [1], the dependence of the discharge time in crystals on thickness was constructed (Fig. 1). The stepwise change in the discharge time at a thickness \(d_{\mathrm{cr}} \simeq 10^{-3}\) cm is the result of a change in the discharge mechanism. The large value of the discharge time at a thickness of \(10^{-3}\)—\(10^{-4}\) cm indicates a multi-avalanche discharge mechanism, which is also confirmed by the decrease in breakdown voltage with increasing intensity of cathode irradiation [2]. Studies of the discharge delay time \(t_{\mathrm{del}}\) in thin layers of ionic crystals [3] at \(d \simeq 10^{-3}\) cm yielded \(t_{\mathrm{del}}\) on the order of several microseconds and gave—
a marked decrease in the discharge delay time with increasing overvoltage \(\beta\) (Fig. 2), where
\[ \beta=\frac{U}{U_{\mathrm{st}}}, \]
\(U_{\mathrm{st}}\) is the static breakdown voltage corresponding to a breakdown probability \(\psi=90\%\).
In the single-avalanche mechanism of discharge development at \(d=d_{\mathrm{cr}}\), the discharge development time was not measured directly; it was assumed to be equal to \(10^{-8}\) sec (Fig. 1). We attempted to measure the discharge development time for the single-avalanche and multi-avalanche mechanisms of discharge development at a thickness close to the critical one, in order to confirm the discontinuity in time by several orders of magnitude caused by the change in the discharge mechanism.
Fig. 1. Dependence of the discharge time in NaCl, KCl, and KBr crystals on thickness.
Fig. 2. Dependence of the discharge delay time \(t_{\mathrm{del}}\) on overvoltage \(\beta\):
1 — KBr, \(d=7\ \mu\); 2 — KBr, \(d=10\ \mu\);
3 — NaCl, \(d=6.15\ \mu\);
4 — NaCl, \(d=11.5\ \mu\).
Experimental Method
Rock-salt samples of thickness \(d \simeq d_{\mathrm{cr}} = 30\ \mu\), with liquid electrodes prepared by the method of [4], were studied under rectangular voltage pulses with a front duration of the order of \(5\cdot10^{-7}\) sec, obtained using a single-stage pulse generator.
The breakdown time was measured from the beginning of the pulse to the breakdown instant from oscillograms obtained on a high-voltage electronic oscilloscope at an overvoltage on the sample equal to 5%.
The overvoltage was defined as
\[ \beta=\frac{U_2\cdot100}{U_1+\frac{\Delta U}{2}}\ \%, \]
where \(U_1\) is the amplitude of the pulse that still does not cause breakdown of the sample;
\(U_2\) is the amplitude of the pulse at which breakdown occurred.
The voltage amplitude was determined by the charging voltage of the GIN(a). No more than 2–3 pulses with successively increasing amplitude were applied to each specimen.
Studies [5] have shown that the application of preliminary voltage pulses with an amplitude below the breakdown value, when liquid electrodes are used, does not affect the electrical strength of solid dielectrics. From the tested batch of specimens, numbering \(n=54\), specimens in which breakdown occurred on the flat portion were taken into account. To measure the discharge time in the multiple-avalanche mechanism, a high-voltage electronic oscilloscope with a sweep duration of 25 μsec was used.
The values of \(t_{\text{lag}}\) for a batch of \(n=54\) specimens were statistically processed (Fig. 3). As a result of the investigation, for the multiple-avalanche breakdown mechanism in NaCl at \(d=30\ \mu\) and \(\beta=5\%\), the value
\[ t_{\text{lag}}=3.4\ \mu\text{sec} \]
was obtained.
In the study of \(t_{\text{lag}}\), out of the entire batch of specimens numbering \(n=54\), \(n_1=14\) specimens broke down on the pulse front with a small discharge delay time \(t_{\text{lag}} \leqslant 5\cdot 10^{-7}\) sec.
Fig. 3. Statistical processing of delay times.
A short delay time indicates a single-avalanche discharge mechanism, since in a time less than \(10^{-6}\) sec the multiple-avalanche mechanism does not have time to develop, and breakdown occurs at a higher field strength owing to the formation of one powerful avalanche.
To determine the breakdown time in the single-avalanche mechanism, we changed the pulse parameters—we shortened the front to \(5\cdot 10^{-9}\) sec.
The setup circuit, constructed according to the type developed at the Tomsk Polytechnic Institute [6], is shown in Fig. 4.
A coaxial cable of type RK-3 was used as the pulse-forming element. The switching spark gap was placed in a chamber with nitrogen at a pressure of 8 atm. This generator made it possible to obtain single pulses with a front duration of the order of \(5\cdot 10^{-9}\) sec and an amplitude corresponding to half the charging voltage.
The breakdown time was determined as the difference between the instant of breakdown of the specimen according to the breakdown oscillogram and the instant of arrival of the pulse at the short-circuited load, recorded on the oscilloscope. Since the specimen and the divider connected to the oscilloscope PYa are separated from one another, this factor must be taken into account. The studies showed that
of the batch of investigated specimens, numbering \(n=59\), a part \(n_1=31\) broke down on the front, while the rest \(n_2\)—behind the screen of the oscilloscope. In these specimens, in all probability, a multichannel-streamer discharge mechanism with a long delay time was realized.
Fig. 4. Schematic of the setup for investigating \(t_{\mathrm{del}}\).
According to our investigations, the development time of the discharge for a single-channel discharge mechanism amounted to no more than the length of the pulse front, i.e., less than \(5\cdot 10^{-9}\) sec. For verification, a batch of specimens was punctured with a longer sweep of the recorded pulse, equal to \(0.3\ \mu\)sec. The same separation in the development time of the discharge was obtained.
One part of the specimens broke down on the front, \(n_1\), the other, \(n_2\)—behind the screen of the oscilloscope; no breakdown delay times within the duration of the \(0.3\ \mu\)sec sweep were observed. Then we proceeded to investigations with an oscilloscope sweep of \(0.1\ \mu\)sec in order to estimate the development time of the discharge for a single-channel mechanism, which proved to be less than \(5\cdot 10^{-9}\) sec, and to measurements of \(t_{\mathrm{del}}\) for the multichannel discharge mechanism with a sweep of \(25\ \mu\)sec, which was estimated as \(3.4\cdot 10^{-6}\) sec.
Fig. 5. Dependence of the probability of breakdown \(\varphi\%\) with a long delay time on overvoltage \(\beta\%\).
Further investigations were carried out for several batches of specimens at overvoltages \(\beta=5;\ 10;\ 20;\ 50\%\), and the probability of breakdown with a long delay time (multichannel-streamer mechanism) was estimated.
With increasing \(\beta\), the number of specimens breaking down on the front increases, and at \(\beta=50\%\) all specimens from the investigated batch break down on the pulse front with a delay time less than the duration of the pulse front, \(5\cdot 10^{-9}\) sec. Fig. 5 illustrates the character of the variation \(\varphi=f(\beta)\), where \(\varphi=\dfrac{n}{n_2}100\%\), \(\beta\) is the overvoltage in %.
Our investigations experimentally confirm the difference in the discharge development times at \(d\approx d_{\mathrm{cr}}\), for one and the same overvoltage on the specimen.
In the case of the single-avalanche mechanism, \(t_{\text{del}}\) is less than \(5 \cdot 10^{-9}\) sec, whereas for the multi-avalanche mechanism the discharge development time was estimated as \(3.4\ \mu\text{sec}\). The abrupt change in the discharge development time by several orders of magnitude confirms the change in the discharge mechanism in solid dielectrics.
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