Dielectric Breakdown Analysis
Dielectric Breakdown: Theoretical Foundations
Dielectric Breakdown
Professor, is dielectric breakdown when the electric field is too strong and the insulator breaks down?
Yes. When the electric field strength exceeds the dielectric strength (breakdown field strength), insulation breaks down and discharge occurs.
Dielectric Strength Reference
| Material | Dielectric Strength [kV/mm] |
|---|---|
| Air (1atm) | 3.0 |
| SF₆ (0.1MPa) | 8.9 |
| Transformer Oil | 10–20 |
| Epoxy Resin | 20–30 |
| Polyethylene | 20–50 |
| SiO₂ (thin film) | 500–1000 |
SiO₂ thin film is orders of magnitude stronger!
Thin films have high strength due to fewer defects. However, at thicknesses of a few nm, leakage current flows due to the quantum tunneling effect.
Paschen's Law
The breakdown voltage of a gas is a function of the product $pd$ of pressure $p$ and electrode gap distance $d$:
$A, B$: gas constants, $\gamma$: secondary electron emission coefficient. There is a minimum value (Paschen minimum) for $pd$.
Summary
- Breakdown when Electric Field > Dielectric Strength — varies by material
- Paschen's Law — breakdown voltage for gases
- Calculate electric field distribution with FEM → Compare with dielectric strength — basic flow of insulation design
Townsend Avalanche—Understanding Lightning's "Avalanche" at the Quantum Level
The Townsend electron avalanche theory (early 1900s), fundamental to gas insulation breakdown theory, describes the process where one electron accelerates and collides with a neutral molecule → new electrons and ions are generated → these further accelerate → electron number increases exponentially. The exponential growth coefficient (Townsend's first ionization coefficient $\alpha$) depends on the electric field and gas pressure, giving rise to the pressure and gap dependence of the breakdown voltage. Lightning is a Townsend avalanche on a massive scale.
Computational Methods for Dielectric Breakdown
Dielectric Breakdown FEM
FEM does not directly calculate "breakdown"; rather, it calculates the electric field distribution and compares it with the dielectric strength.
1. Obtain electric field $E$ via electrostatic field analysis
2. Check if $E < E_{breakdown}$ throughout the entire domain
3. Evaluate safety factor $SF = E_{breakdown} / E_{max}$
How much safety factor is needed?
| Application | Recommended Safety Factor |
|---|---|
| Power Equipment (IEC Standards) | 2.0–3.0 |
| Automotive (AEC-Q Standards) | 2.0 or higher |
| Aerospace | 3.0 or higher |
| Consumer Products | 1.5–2.0 |
Summary
- FEM Electric Field Analysis + Dielectric Strength Comparison — breakdown judgment
- Safety Factor 2–3 is standard — varies by application field
Paschen's Law—Discharge Voltage Determined by "Product of Pressure and Electrode Gap"
The breakdown voltage of a gas follows the "Paschen curve" (discovered in 1889), uniquely determined by the product of gas pressure $p$ and electrode gap $d$ (the $pd$ product). A minimum breakdown voltage (Paschen minimum) exists; for air, it's about 330V at approximately 1cm electrode gap and 1 atm. The breakdown voltage increases for gaps narrower or wider than this. Understanding this law helps answer questions like "Why is insulation more difficult at low pressure?" in equipment design for high altitudes (low pressure) or vacuum insulation design.