Breakdown mechanisms in solids, explain one

Breakdown of a solid dielectric is the permanent failure of its insulation when the electric stress exceeds its strength. The mechanism depends on the time for which the voltage is applied.

Mechanisms of breakdown in solids in practice

In equipment in service, the long-time mechanisms (thermal, chemical, treeing/tracking and internal discharges) are responsible for most failures, because the working stress is well below the intrinsic strength.

Thermal breakdown (explained)

Cause. Every dielectric loses some energy as heat: conduction loss under DC and dielectric loss ($\tan\delta$) under AC. For most insulators conductivity increases with temperature, so heating increases losses, which increases heating further.

Heat generated per unit volume:

$$\begin{aligned} W_{dc} &= \sigma E^2 \\ W_{ac} &= \frac{E^2 f\,\varepsilon_r\tan\delta}{1.8\times10^{12}}\ \text{W/cm}^3 \end{aligned}$$

Heat balance in a small volume:

$$C_v\frac{dT}{dt} + \text{div}(K\,\text{grad}\,T) = \sigma E^2$$

where $C_v$ is the specific heat per unit volume and $K$ the thermal conductivity.

Stable and unstable states.

Heat generated rises roughly exponentially with temperature, while heat dissipated rises roughly linearly with $(T - T_0)$:

At $E_1 > E_2$ the temperature rises without limit and the material melts, chars or burns (thermal runaway).

Features.

• Thermal breakdown voltage falls with rising ambient temperature and with poor cooling.
• Under AC it is lower than under DC, because dielectric loss rises with frequency.
• Thick insulation is worse cooled at the centre, so strength per mm falls with thickness.
• Typical thermal breakdown strengths: about 3–5 MV/cm (DC) and 1–3 MV/cm (AC) for good polymers; much lower for high-loss materials like glass at high temperature.

Thermal breakdown is controlled by using low-loss materials (low $\tan\delta$), good cooling and limiting the operating temperature (insulation class limits).