Kramers–Kronig Diagnostic of Humidity-Induced Non-Idealities in Nanostructured Silica Capacitors

Metal–insulator–metal capacitors based on electrosprayed silica nanoparticles exhibit exceptionally high effective permittivity. However, their dielectric response is highly sensitive to ambient humidity, which can compromise data reliability. This study analyzes impedance characteristics of two silica nanoparticle-based MIM capacitors: (i) one measured under ambient conditions (0.1 Hz to 2 MHz) at 100/500 mV, and (ii) another under controlled relative humidity (RH) (40%, 70% and 90%) at 500 mV. Impedance consistency is rigorously assessed via Kramers–Kronig (KK) transforms. The first capacitor shows excellent KK consistency for real part Z′ (NRMSE = 3.3%), compatible with linear time-invariant assumptions. The second capacitor exhibits strong humidity-dependence deviations; NRMSE for Z′ rises from 14.5% at 40% RH to 141.2% at 90% RH, indicating linearity/causality breakdown from moisture-induced ionic conduction and interfacial polarization. These findings demonstrate that while increased humidity amplifies the effective dielectric response, it simultaneously introduces non-idealities that invalidate standard KK assumptions. Due to inherent microstructural variability between devices, humidity-dependent conclusions are derived from controlled intra-device analysis. Transmission Line Modeling confirms moisture enhances ionic network connectivity. Thus, KK analysis serves as a sensitive probe of environmental effects on nanostructured dielectrics, offering a framework to diagnose non-ideal behavior without a priori equivalent circuit models.