An electro-thermal approach to dielectric breakdown in solids: Application to crystalline polymer insulators

A dielectric breakdown model, linked to appearance of a singularity, has been developed and applied to a high purity alkane type (n-C₃₆H ₇₄) insulator. The polymer material, which exhibits low defect / trap density, represents the single-crystalline iso-electronic analog to polyethylene. At high fields, and based on experimental findings, carrier transport is mediated by delocalized states in the conduction and valence band, respectively. Field induced impact ionization and carrier multiplication are triggered by hot carrier photoinjection above a critical field magnitude of 0.8 MV for holes and 1.26 MV for electrons, in accord with the band model. Associated critical sample thickness values have been estimated. The related electrical properties have been explored on the basis of the electrothermal heat balance equation. The non-linear differential equation has been solved numerically, with appropriate thermo-physical materials and carrier transport parameters, considering the dielectric breakdown phenomenon as a singularity. It leads to thermal run-away as a consequence of strong positive electro-thermal feedback, under conditions of initial transient behavior. Required thermo-physical parameters are attributed to and explain filamentary charge transport. The temporal evolution of temperature and current in the conducting filament during the breakdown event exhibits a time scale up to the microsecond range. The dynamic properties of the phenomenon are strongly affected by heat transfer from the conducting section into the surrounding nonconducting material, as well as the temporal characteristics of the initial trigger conditions.