Refined dielectric breakdown model for crystalline organic insulators: electro-thermal instability coupled to interband impact ionization

Abstract

A refined, substantially improved dielectric breakdown model is presented and applied to solution grown, single crystalline alkane type polymeric (n-C36H74) insulator, representing the iso-electronic analog to polyethylene. Ultraviolet illumination of attached electrodes allows controlled generation, injection into and transport of free charge carriers through the insulator. At sufficiently high electric fields, carrier transport is mediated by delocalized states in the conduction and valence band, respectively. At low and moderate fields, charge transport is suppressed by carrier trapping effects. Electric field induced inter-band impact ionization and generation of electron-hole pairs has been identified from these experiments as the dominant carrier multiplication and breakdown triggering mechanism. Critical field magnitudes >;1.26 MV/cm have been recorded experimentally for injected electrons and >;0.8 MV/cm for defect electrons, in reasonable agreement with the theoretical model. Application of the energy conservation principle, in accord with the solid state band model, allows determination of critical fields from the insulators electronic band-gap, effective mass and mobility of minority charge carriers. The related electrical breakdown feature and associated rapid dynamic temperature evolution has been explored on basis of the electro-thermal heat balance equation, following previous concepts applied to phase transitions. The non-linear differential equation has been solved numerically, using appropriate thermo-physical materials parameters, while considering the dielectric breakdown phenomenon as a singularity of the solution. Thermal and current run-away is due to strong positive electro-thermal feedback, in connection with an initial transient resistive behavior. Very small thermo-physical parameters are attributed to and explain filamentary charge transport. The temporal evolution of temperature and current in the conducting section or filament during the breakdown event exhibits a time scale up to the microsecond range. Shock wave emission is apparent, since the spatial temperature propagation exceeds the velocity of sound.