Notes on capacitors

Alumina capacitor

Alumina

Alumina or aluminium oxide (Al2O3) seems to have good properties to be used as insulator to build a capacitor.

Aluminium oxide characteristics:

  • density: 3.987 kg/dm3
  • thermal conductivity: 30 W.m-1.K-1
  • dielectric strength: 14.6 MV.m-1
  • relative permittivity: 9.0

Insulator thickness for a breakdown voltage of 3.5V:

\[\frac{3.5}{14.6 * 10^6} = 0.24 * 10^{-6} m = 0.24 \mu m\]

Capacitor geometry

We consider a a stack of parallel-plate capacitor.

  • Insulator layer thickness: 0.24 um
  • square surface of 0.1 m x 0.1 m = 0.01 m2
  • height: 0.1 m
  • volume: 0.1 * 0.1 * 0.1 = 1 dm3 = 1 L
  • mass: 1.0 * 3.987 = 4 kg
  • number of layers:
\[\frac{0.1}{0.24 * 10^{-6}} = 416000 layers\]

Capacitance

For one layer:

\[C = \epsilon_0 * \epsilon_r * \frac{surface}{thickness} = 8.85 * 10^{-12} * 9.0 * \frac{0.01}{0.24 * 10^{-6}} = 3.31 * 10^{-6} F\]

For the complete capacitor:

\[416000 * 3.31 * 10^{-6} = 1.38 F\]

Energy

Stored energy at 3.0V:

\[E = \frac{1}{2} * C * u^2 = 0.5 * 1.38 * 3^2 = 6.2 J = 0.0017 Wh\]

Specific energy

\[\frac{6.2 J}{4.0 kg} = 1.55 J/kg = 0.00043 Wh/kg\]

Energy density

\[\frac{6.2 J}{1.0 L} = 6.2 J/L = 0.0017 Wh/L\]

Commercial ultracapacitors

Skeleton technologies

https://www.skeletontech.com/

According to their datasheet:

  • Specific energy: 5.3 Wh/kg
  • Energy density: 6.4 Wh/L

Conclusion

The naive approach with alumina insulator provides poor result compare to the current state of the art of the industry.

  • Specific energy ratio:
\[\frac{5.3}{0.00043} = 12325\]
  • Energy density ratio:
\[\frac{6.4}{0.0017} = 3764.7\]