Analytical Time-Domain Models for the Analysis of Tapered Differential Multibit TGVs for 3D ICs

In this paper, tapered differential multi-bit through glass vias (DM-TGVs) utilizing mixed carbon-nanotube (CNT) bundle (MCB) as fillers are presented for three-dimensional (3D) integration. Analytical expressions of resistance, inductance, conductance, and capacitance for tapered DM-TGVs are computed. Using the matrix-rational approximation technique, time-domain analysis of tapered DM-TGVs is examined which includes in-phase and out-phase switching delays, functional crosstalk at different tapered angles and temperature, for different MCB arrangements. It is found that tapered DM-TGV with a single layer of single-wall CNTs at the periphery only and rest filled with multi-walled MWCNTs (m
F
-TGV) demonstrate better transient response in comparison to other TGV configurations. It can be anticipated that tapered DM-TGVs can help alleviate signal reliability issues in 3D ICs, which demonstrate better signal transmission characteristics.