Predicting substrate resonance mode frequency shifts using conductive, through-substrate vias

Abstract

Through-substrate-vias (TSVs) provide conduction paths to allow for three-dimensional integration of microelectronic structures. It is also known that metallic TSVs can be used to suppress resonance modes within dielectric substrates by altering the propagation of electromagnetic waves. Numerical analyses of transmission through substrates containing metallic TSVs revealed that although resonance modes of the composite structure are shifted to higher frequencies, these frequencies are not solely dictated by the TSV periodicity. Simulations show that hybrid modes are formed through a convolution of the original substrate modes and a long-wavelength mode analogous to that found in a two-dimensional photonic crystal. An analytical formula is proposed that provides a simple relation between the intrinsic substrate mode frequencies and the long-wavelength mode that scales with the ratio of TSV radius to its periodicity.