Directional Effects in the Electric Breakdown of Ionic Crystals

A theory is proposed to explain the fact that in ionic crystals the paths formed as a result of electric breakdown lie along definite crystallographic directions which are independent of the direction in which the breakdown field is applied. The directional dependence of the collision probability for fast electrons is calculated on the basis of the directional asymmetry of the Brillouin zone of the phonons and the selection rules for electron-phonon collisions. For increasing temperature, or increasing impurity content, or decreasing overvoltage, the theory predicts the following sequence of breakdown directions: $\mathrm{Random} [R]\ensuremath{\rightarrow}[100]\ensuremath{\rightarrow}[111]\ensuremath{\rightarrow}[110]\ensuremath{\rightarrow}[110] \mathrm{and} [100]\ensuremath{\rightarrow}[100].$ A criterion is suggested for predicting the paths to be observed under any given conditions.