# Dielectric breakdown characteristics of alumina

Fatiha Talbi, Fadila Lalam, David Malec

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Fatiha Talbi, Fadila Lalam, David Malec. Dielectric breakdown characteristics of alumina. ICSD 2010: 10th IEEE International Conference on Solid Dielectrics, Jul 2010, Potsdam, Germany. pp.1-4, 10.1109/ICSD.2010.5568235. [hal-03966145](https://hal.science/hal-03966145v1)

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# Dielectric Breakdown Characteristics of Alumina

Fatiha Talbi and Fadila Lalam

Quntium Chemistry and Physics Laboratory
Mouloud Mammeri University

Tizi-Ouzou, Algeria
talbifatiha@yahoo.fr

David Malec

Laplace Laboratory
Paul Sabatier University

Toulouse, France

**Abstract** The AC 50 Hz sine dielectric breakdown of alumina ceramics versus thickness (0.127 to 2.54 mm) and purity (92%, 96% and 99.5%) was investigated. The results have shown that the dielectric strength decreases with the thickness and increases with the purity. Furthermore, the investigation of the failure morphology using the scanning electron microscopy (SEM) show for each specimens submitted to breakdown the presence of a canal terminated by a crater at the surface. This crater is resulting from the extraction and ejection of the matter during the breakdown process caused by the intensification of the local electric stress. An evolution of the crater size versus the sample thickness have also been observed. The analysis of the experimental results and the SEM observations confirm that the built up of the crater is a crucial step in dielectric breakdown process and the mechanism best suited to describe the dielectric breakdown in these materials is based on an electromechanical one.

**Keywords** alumina; dielectric breakdown mechanism; crater

## I. INTRODUCTION

Ceramic-based alumina materials seem to be a good candidate to ensure electrical isolation in extreme environment conditions because of their high electrical strength, chemical stability and high thermal conductivity. However, the use of these materials is still limited by their brittleness (i.e. low tenacity). Different phenomena can induced a dielectric breakdown in insulators subjected to high electric stress: thermal, electronic and electromechanical breakdown. The occurring one of them depends strongly on the physical properties of the material. In the case of alumina ceramics, because of the brittleness, the mechanical instability is quickly reached and the dielectric properties are affected. Numerous works have suggested that the dielectrics properties of alumina may be closely related to its mechanical ones [1-2]. The mechanism best suited to describe the dielectric breakdown of alumina is the electromechanical one. Under a high electrical field, the electromechanical generation and growth of defects in ceramics is the main causes of the initiation of the breakdown process.

The purpose of this paper is to study the morphological features of dielectric breakdown of alumina in order to define and validate the breakdown mechanism.

## II. EXPERIMENTAL

### A. Materials under study

The dielectric breakdown of polycrystalline α-alumina samples having different purities (92, 96 and 99.5 %) and different thicknesses (127 µm to 2.54 mm) have been investigated. Laser Induced Breakdown Spectroscopy has been used to estimate both nature and content of impurities. The major impurities present in alumina depending purity is reported in table 1.

As the dielectric breakdown of polycrystalline Alumina depends on its grain dimensions, samples have been chosen with mean grain size of 5 µm.

Alumina substrates have been cut into samples having a section of one inch in order to be tested in the measuring cell.

### B. Experimental setup

The experimental setup for dielectric breakdown measurement is classically composed of high voltage transformer driven by a motorized autotransformer. A current detection is used to detect any breakdown event occurring in the sample in order to switch-off the high voltage. The measuring cell is detailed in figure 1. The diameter of the two plane electrode is of 15 mm and the radius of the half-spherical electrode is of 0.6 µm. These electrodes are stainless steel. The electrodes system (plane/plane or plane/half-spherical) is immersed in insulating perfluorinated liquid in order to prevent any flashover or partial discharge on the sample surface. All measurements presented in this study are at room temperature.

<table><caption>TABLE 1. Wt % major content of impurities (635 µm thick Alumina samples).</caption><thead><tr><th>Al<sub>2</sub>O<sub>3</sub> 92%</th><th>Al<sub>2</sub>O<sub>3</sub> 96%</th><th>Al<sub>2</sub>O<sub>3</sub> 99.5 %</th></tr></thead><tbody><tr><td>Mn: 1.61</td><td>Si: 1.10</td><td>Mg: 0.16</td></tr><tr><td>Si: 1.1</td><td>B: 0.86</td><td>Ca: 0.15</td></tr><tr><td>Fe: 1.06</td><td>Mg: 0.47</td><td>Si: 0.13</td></tr><tr><td>Ti: 1.00</td><td>Ca: 0.21</td><td>Fe: 400 ppm</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>Figure 1. Breakdown measuring cell.</figcaption></figure>

### C. Experimental results of breakdown strength

The experimental results of AC breakdown strength (rms values) depending thickness and purity of alumina are reported in fig. 2 and fig. 3 respectively. These breakdown experiments were performed using plane-spherical system of electrodes with a voltage rise rate of 1.6 kV/s.

These results are Weibull's statistical values obtained from 20 breakdown tests for each Alumina thickness and purity. For each breakdown value, its corresponding 90 % confidence interval has been plotted. As expected [3-4], the electrical breakdown strength (E<sub>b</sub>) of alumina is strongly dependent on the sample thickness (d) and can be described by the well-known inverse power-law relation:

$$E_b = Ad^{-n} \quad (1)$$

The curve fitting analysis of data points (fig. 2) leads to the following expressions:

<figure><img src="image_3.png" /><figcaption>Figure 2. Dielectric strength of polycrystalline Alumina samples versus thickness.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3. Dielectric strength of 635 µm thick polycrystalline Alumina versus alumina content (%).</figcaption></figure>

$$\text{Alumina 96\%: } E_b = 569d^{0.51}. \quad (2)$$

$$\text{Alumina 99.5\%: } E_b = 992d^{0.57}. \quad (3)$$

Both A and n parameters are found to be purity dependent.

Fig. 3 indicates that the electrical breakdown strength is also dependent on the purity: the higher the purity, the higher the breakdown strength, but it seems not to be affected by the nature of impurities.

### D. Optical and SEM observations

All samples subjected to breakdown have been inspected by using a microscope. Irregular breakdown channel (fig. 5) terminated by a crater (fig. 6) at the surface have been observed on samples. For plane-plane electrodes, this crater is located indifferently on either one surface or on the other, while for half spherical-plane electrodes, it is always located at the point where the half spherical electrode touch the sample surface.

<figure><img src="image_5.png" /><figcaption>Figure 4. Surface breakdown morphology of a 1.016 mm thick alumina sample: crater.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5. Cross section of breakdown channel of a 254 µm thick alumina sample.</figcaption></figure>

The analysis of these results indicates that the crater takes place on the alumina surface where the electric is the highest or where an initiating defect may be found as in the case of a plane-plane electrode system.

### III. DISCUSSION

#### A. Mechanical origin of breakdown

The common point of the observation of post-mortem alumina samples is the appearance of crater at the surface however some samples exhibit a surface damage as shown in fig. 6.

The extracted matter, leading to the formation of craters, was examined by microscopy analysis. As clearly shown by these observations no solidified molten matter trace was found, suggesting that the crater was formed before the dielectric breakdown to occur [5].

In first approximation, the craters are supposed to have the shape of cones then a statistical of craters size has been

<figure><img src="image_7.png" /><figcaption>Figure 6. Surface breakdown morphology consisting of not emptied crater on a 1.016 mm thick 96 % alumina sample.</figcaption></figure>

performed in order to estimate their evolution versus thickness. The results are reported in fig. 7.

As clearly shown in fig. 7, the evolution of the craters diameter versus thickness is not obviously random and found to have a nonlinear evolution versus thickness. Note that the SEM observations reveal that the crater depth is in the same order of magnitude as the radius crater.

#### B. Dielectric breakdown modeling

The balance concept of fracture, originally proposed by Griffiths [6], inspired numerous researchers to interpret the mechanical origin of solid dielectric breakdown [7-8]. According to this concept, the dielectric breakdown is based on crack propagation driven by release of both electrostatic energy and electromechanical strain energy. This mechanical crack propagation induced the dielectric breakdown to occur when the work done by the mechanical forces exceeds the crack propagation energy.

When the electric field E is applied to the tested sample, a resulting electrostatic energy density of $0.5\epsilon E^2$ takes place. The corresponding mechanical stress, induced by this electrostatic field, is then $\sigma = 0.5\epsilon E^2$. Consequently, the total energy density, made of both electrostatic and electromechanical components, is given by the relationship:

$$W_{es}+W_{em}=0.5\epsilon E^{2}+(\sigma^{2}/2Y) \quad (4)$$

Where $\epsilon$ is the dielectric constant and Y the young modulus of material. By replacing $\sigma$ in (4), the total energy density becomes:

$$W_{es}+W_{em}=0.5\epsilon E^{2}+(\epsilon^{2}E^{4}/8Y) \quad (5)$$

Taking into account the value of Y, it can be easily seen that the electrostatic component dominates if $E<10^{11}$ V/mm, which is obviously the case for alumina at breakdown. According to an electric analogous Griffith criterion, the mechanical breakdown takes place when the electrostatic energy released becomes greater than the energy requires to create new surfaces, given by $\gamma\delta s$ where $\gamma$ is the surface free energy, as a crack propagates. This leads to the relationship:

<figure><img src="image_8.png" /><figcaption>Figure 7. Evolution of craters size versus 96% and 99.5% Alumina samples thickness.</figcaption></figure>
$$0.5\varepsilon E^2 \partial v > \gamma \partial s. \qquad (6)$$

$\partial v$ and $\partial s$ represent the unit volume and surface of the infinitesimal crack growth increment respectively. $\partial v$ can be related to $\partial s$ by the following equation:

$$\partial v = \alpha \partial s. \qquad (7)$$

Where $\alpha$ is a geometric factor determined by the crack or flaw shape and $\alpha$ is the largest flaw size.

Substituting (7) into (6) leads to a critical field $E_c$ given by:

$$E_c = (\alpha)^{-1/2} (2\gamma/\varepsilon\alpha)^{1/2} \qquad (8)$$

Where $(\alpha)^{-1/2}$ is of order of unity.

Surface free energy values of alumina was determined using the optical goniometer. The principle consists in measuring the contact angle values for alumina sample surface and standard liquids with known values of surface energy and then solving the Owen-Wendt equation [9]. The surface energy values obtained for alumina samples under study are of the order of magnitude of 55 mJ/m².

Taking a equal to 5 µm which is of the same order of magnitude as grain size of alumina under study, the critical field predicted by (8) is found to be equal to 16.7 kV/mm which is consistent with experimental results. Moreover, (8) show that an evolution of the theoretical dielectric strength with thickness implies an evolution of the defect size $\alpha$ with the thickness in the same tendency of that crater size (fig. 7).

## IV. CONCLUSION

The dielectric strength of polycrystalline $\alpha$-alumina samples having different thickness and purity has been measured. For each sample subjected to dielectric breakdown, a crater has been observed at the vicinity of the breakdown channel. The crater size has been estimated using optical observations. The results have revealed that the size of alumina samples craters versus thickness is not random but follows a nonlinear evolution. Moreover, molten matter originated from the breakdown channels has only been copiously observed on the craters surface, suggesting that the explosion event leading to the extraction of matter occurs before dielectric breakdown. The electromechanical model proposed to describe the dielectric breakdown is in good agreement with experimental results but further work is necessary to investigate the surface energy properties and the relationship between defect size and crater size.

## REFERENCES

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