A robust determination of the effective thermal conductivity of a multilayer Si3N4/SiO2 stack using multiple heater...

Multilayer dielectric thin films are fundamental components in modern microelectronic and photonic devices where thermal management is critical. This work presents a robust methodological framework for accurately determining the cross-plane effective thermal conductivity (κeff,⊥) of such complex systems using the 3-omega method. We use a five-layer Si3N4/SiO2 stack fabricated by plasma-enhanced chemical vapor deposition as a case study. The analysis combines experimental data from multiple heater geometries with a 3D finite element method based inverse analysis. We first demonstrate, through a frequency-dependent sensitivity analysis, that a direct multi-parameter fit for intrinsic layer properties is an ill-posed problem. This analysis provides a clear, quantitative justification for adopting a simpler and more robust effective medium model (EMA). The validity and application boundaries of the EMA are then rigorously established through a numerical study on a series of "virtual samples." Finally, applying this validated framework to our experimental data, the thermal conductivity of a fused silica substrate was determined to be 1.287 ± 0.030 W/(m K), and the effective thermal conductivity of the 1288 nm thick stack was reliably determined to be 0.621 ± 0.008 W/(m K). This work provides not only a key thermophysical property for Si3N4/SiO2 multilayers but also a comprehensive and validated workflow for reliably characterizing complex thin film systems where standard analytical solutions fail.