Thermally tunable high-voltage breakdown and divergent avalanche nonlinearity in planar SnO₂ nanofilm varistors

We present a planar, dopant-segregation-free SnO₂ nanofilm varistor on a polycrystalline Al₂O₃ substrate that achieves a kilovolt-level breakdown voltage (V_{1 mA} ≈ 759 V at 300 K). By directing the conduction pathway laterally across approximately 200 grain boundaries in series, this architecture overcomes the low-voltage limitations of conventional vertical thin films. Within the compliance-limited window, the device exhibits a pronounced divergent nonlinearity without bulk-resistance rollover. This steep current rise is analytically identified as an avalanche-type divergence, α (V) = V / (V* − V), driven by an electro-thermally assisted barrier collapse under localized Joule heating. To capture the full I–V trajectory across 200–500 K, we formulate a cascade model employing logistic soft-switch weights to govern the competitive transitions among Ohmic leakage, thermionic emission, and avalanche multiplication. The critical divergence voltage V* follows a strict Arrhenius scaling with an effective activation energy of ∼33 meV, reflecting how ambient thermal energy exponentially accelerates the pre-breakdown conductivity to reach the thermal runaway threshold. This planar nanofilm provides a lithographically defined, circuit-compatible platform, complementary to bulk ceramics, for on-chip transient voltage suppression.