Time-Dependent Effects in Disordered Materials pp 103-106 | Cite as

# Theory of Dielectric Breakdown in Metal-Loaded Dielectrics

## Abstract

We have examined a very simple model of dielectric breakdown in random mixtures of metal and dielectric.^{1,2,3} We expect this analysis to be relevant for an class of materials which are composed of a random mixture of metallic particles embedded in a dielectric matrix. An example is solid fuel rocket propellant^{4} which is a mixture of microscopic aluminum particles (the fuel) in a dielectric matrix composed of oxidizer and rubber binder. The model we analyze is a percolation model in which the bonds of a d-dimensional lattice with lattice spacing a are occupied by conductors with probability p and by capacitors with probability 1-p. The probability p is chosen to be less than the percolation threshold p_{c} so that no conducting path traverses the entire system. The breakdown process is modeled by assuming that the capacitors can withstand a maximum voltage drop of 1 volt. The entire lattice has a size of L lattice spacings. A macroscopic voltage is applied across the lattice. This voltage is raised until the voltage drop across one of the capacitors exceeds 1 volt. This macroscopic voltage is called V_{1} the initial breakdown voltage. The capacitor which fails is replaced by a conducting element. The process of failing one of the capacitors is repeated until a conducting path is formed across the sample. The maximum value of the applied voltage during this procedure is called the complete breakdown voltage and is denoted V_{b}.

## Keywords

Percolation Threshold Conducting Path Metal Fraction Dielectric Breakdown Breakdown Field## Preview

Unable to display preview. Download preview PDF.

## References

- 1.D. Bowman, private communication and preprint (1987); H. Takayasu, Phys. Rev. Lett. 54, 1099 (1985)Google Scholar
- 2.L. de Archangelis, S. Redner and H.J. Hermann, J. de Phys. Lett. 46, L585 (1985);CrossRefGoogle Scholar
- 3.P.M. Duxbury, P.D. Beale and P.L. Leath, Phys. Rev. Lett. 57, 1052 (1986);ADSCrossRefGoogle Scholar
- P.M. Duxbury, P.L. Leath and P.D. Beale, Phys. Rev. B, in press (1987);Google Scholar
- P.D. Beale and P.M. Duxbury, submitted to Phys. Rev. B. (1987).Google Scholar
- 4.R. Kent and R. Rat, J. Electrostatics 17, 299 (1985).CrossRefGoogle Scholar
- 5.W. Weibull, “Fatigue Testing and Analysis of Results,” ( Pergamon, New York, 1962 ).Google Scholar