Heat Transfer in Porous Low–k Materials: Modeling Based on Fractional Calculus and Material Structure Fractality

The influence of fractal pore structures on heat transfer in porous low –k films, focusing on organosilicate (OSG) materials with porosity near the percolation threshold, is investigated. Thermal transport deviates from classical behavior at length scales comparable to characteristic pore sizes, with effective thermal conductivity governed not only by porosity but also by the topology of the pore network. Fractal organization of the pores modifies phonon scattering, producing measurable non-classical thermal behavior. Fractional-order heat transport models capture these effects, revealing that the observed deviations arise from a broad, hierarchical distribution of transport length scales. Our results highlight that engineered multiscale pore architectures can be used to tailor thermal transport in low –k dielectric materials. Analytical expressions for the effective thermal conductivity tensor, incorporating finite pore lengths and the fractal nature of the network, are derived, providing a predictive framework for designing porous dielectrics with controlled thermal properties.