Breakdown mechanisms in solids, explain two

Breakdown of a solid dielectric is the permanent loss of its insulating property when the applied stress exceeds what it can withstand; unlike gases and liquids, a solid does not recover after breakdown.

Mechanisms of breakdown in solids

1. Intrinsic (electronic) and avalanche breakdown
2. Electromechanical breakdown
3. Thermal breakdown
4. Electrochemical (chemical) breakdown
5. Breakdown due to treeing and tracking
6. Breakdown due to internal (partial) discharges

Intrinsic and electromechanical breakdown occur in very short times (about $10^{-8}$ s) at high stress, mostly in laboratory conditions. In practical equipment, failure is mostly due to thermal breakdown, chemical deterioration, treeing/tracking and internal discharges, which act over long periods at moderate stress.

1. Thermal breakdown

Every dielectric has losses: conduction loss under DC and dielectric loss under AC. The heat produced raises the temperature; in most insulators conductivity rises with temperature, so losses rise further.

• Heat generated per unit volume:
  • DC: $W_{dc} = \sigma E^2$
  • AC: $W_{ac} = \dfrac{E^2 f\,\varepsilon_r \tan\delta}{1.8\times10^{12}}$ W/cm³ ($E$ in V/cm)
• Heat balance:

$$\underbrace{\sigma E^2}_{\text{generated}} = \underbrace{C_v\frac{dT}{dt}}_{\text{stored}} + \underbrace{\text{div}(K\,\text{grad}\,T)}_{\text{conducted away}}$$

• If the heat generated stays below the heat dissipated, a stable temperature is reached. If it exceeds it at all temperatures, temperature rises without limit (thermal runaway) and the material melts or burns.

The heat-generated curve rises steeply (exponentially) with temperature, while the heat-dissipated curve rises roughly linearly. Breakdown occurs at the field where the two curves just touch.

Since AC loss is proportional to frequency, thermal breakdown voltage under AC is lower than under DC.

2. Electromechanical breakdown

When a voltage is applied, the electrodes attract each other with electrostatic pressure. A soft material of thickness $d_0$ is compressed to thickness $d$. Equilibrium:

$$\frac{\varepsilon_0\varepsilon_r V^2}{2d^2} = Y \ln\frac{d_0}{d}$$

where $Y$ is Young's modulus. The system becomes unstable when $d/d_0 = 0.6$, giving the highest apparent stress

$$E_{max} = \frac{V}{d_0} = 0.6\sqrt{\frac{Y}{\varepsilon_0\varepsilon_r}}$$

Beyond this the material collapses mechanically and breaks down. This is important for soft polymers (e.g. polythene at high temperature).