Critical Activation Voltage for Phonon-Mediated Field-Driven Phenomena

Field-driven phenomena, from flash sintering to electromigration, exhibit threshold fields spanning eight orders of magnitude. We show that the product of the field and the activation coherence length is a conserved critical activation voltage, V_c = E·r ≈ 0.1–2.7 V, the electrical work required to resonantly couple to the phonon damping peak, closing the thermodynamic barrier for defect generation. This invariant unifies macroscopic to nanoscale thermal and transport instabilities across 17 crystal families.