Theory of Dielectric Breakdown in Metal-Loaded Dielectrics
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 propellant4 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 pc 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 V1 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 Vb.
KeywordsPercolation Threshold Conducting Path Metal Fraction Dielectric Breakdown Breakdown Field
Unable to display preview. Download preview PDF.
- 1.D. Bowman, private communication and preprint (1987); H. Takayasu, Phys. Rev. Lett. 54, 1099 (1985)Google 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
- 5.W. Weibull, “Fatigue Testing and Analysis of Results,” ( Pergamon, New York, 1962 ).Google Scholar