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Method and apparatus for simulating a microelectric interconnect circuit
A method and apparatus for simulating a microelectronic circuit or system includes the storing of a microelectronic circuit or system representation in a computer and then transforming the representation into an equivalent DC circuit containing resistive, capacitive and inductive elements. Then, a directed graph of the DC equivalent circuit is generated and a spanning tree is constructed therefrom. The spanning tree is then actually or virtually traversed to obtain multiple generations of circuit moments. The moments are then used to calculate the poles and residues for a given node and generate an approximate model of the circuit's transient response at that node. Moment shifting is used to provide for a stable approximate model. The actual residues corresponding to the coefficients of the time domain representation for the model can be calculated using the first q-1 moments. This constitutes a partial-Pade approximation.Board of Regents, University of Texas Syste
An investigation of electromigration induced void nucleation time statistics in short copper interconnects
Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The article appeared in the Journal of Applied Physics and may be found at: http://dx.doi.org/10.1063/1.3309744The stress evolution model (SEM) of Korhonenet al., is used to calculate the void nucleation time
in a large number of short interconnects lengths up to 50 um. Finite element calculations show that the effect of the nonlinearity in the SEM model is small, and that a mesh size of the order of
the grain size is quite adequate to give accurate simulation results. Via failure is the only mode considered in the current calculations, however the gain in simulation time over other solution methods means that more complex situations, possibly including void dynamics, may be modeled in future in this way. Using normal mass-lumping methods the analysis is isomorphic to the voltage
development on a random RC chain, so standard methods from very large scale integrated static timing analysis may be used to obtain dominant time constants at each mesh point. This allows the distribution of nucleation times to be obtained as a function of the distributions of line parameters.
Under the assumption of a lognormal grain size distribution and a normal distribution of diffusion
activation energies, the nucleation time distribution is shown to be close to lognormal