3D Substrate/Interconnect Modeling
Pp. 172-211 (40)
Electrical behavior of 3D interconnections (redistribution metal lines, through
silicon via.,) used in 3D IC stack technologies is explored in this chapter. To well
understand the interconnection incidence on 3D system performances, it is important to
consider the whole electrical context of the 3D application, including the silicon substrate.
As an emerging technology, electrical compact models are needed, notably for 3D
interconnects which include Through-Silicon Via, to evaluate with precision 3D systems
performances. However, 3D interconnects introduce several challenges in modeling. As a
matter of fact, they imply considering the whole electrical context by taking into account
for example current paths, couplings between interconnections, couplings with the
substrate. Example of simple closed-form expressions describing electrical model of 3D
ICs propagation lines is reported. We investigate models of high aspect ratio TSV, on both
analytical and numerical methods electromagnetic simulations and RF measurements. This
model enables to extract substrate and TSV impedance and parasitic elements. Its full
compatibility with SPICE-like solvers should allow an in depth investigation of TSV
impact on circuit performance.
Considering the modeling: from any point source, we calculate the impedance spreading
out. For this, our approach is, at least, twofold: compact Green function or Transmission
Line Model, over or into a multi-layered substrate, is derived by solving Poisson's
equation analytically. Rapid evaluation uses the Discrete Cosine Transform and its
variations. Using this technique, the substrate coupling and loss in IC's can be analyzed.
The algorithms permit to extract impedances between any numbers of embedded
contacts. Comparisons are performed, using finite element methods and experiments.
3D, RF, Subtrate/interconnectics, embedded contacts, modeling, TSV,
RDL, analytical model, Poisson’s equation, Green function, FEM, Transmission
Line Method, substrate extractor, electrical experiments, compact models.
Université de Lyon, INSA- Lyon, INL, CNRS France