Physical Consistency of Giant Permittivity in Humid Nanostructured Silica Capacitors via Kramers-Kronig Analysis

Metal-Insulator-Metal (MIM) capacitors based on electrosprayed silica nanoparticles exhibit giant effective permittivity, making them attractive for miniaturized capacitive and sensing. However, their dielectrics response is highly sensitive to ambient humidity, which can compromise data reliability. This study analyzes impedance characteristics of two silica nanoparticles-based MIM capacitors: (i) one measured under ambient conditions across 0.1Hz to 2MHz at 100mV and 500mV excitation, and (ii) another characterized under controlled relative humidity (RH) conditions (40%, 70% and 90%). The physical consistency of the measured impedance is rigorously assessed via Kramers-Kronig (KK) transforms. The first capacitor shows excellent KK consistency for the real part of the impedance (NRMSE=3.3%), indicating behavior compatible with linear-invariant assumptions. In contrast, the second capacitor exhibits strong humidity dependence deviations, NRMSE for Z’ rises from 14.5% at 40%RH to 141.2% at 90%RH, suggesting a breakdown of linearity and causality due to moisture-induced ionic conduction and interfacial polarization processes. These findings demonstrate that while increased humidity amplifies the effective dielectric response, it simultaneously introduces non-ideal effects that invalidate standard KK assumptions. This work underscores the necessity of environmental control and provide critical insights for the design of humidity-sensitive devices and stable insulating capacitors.