Size effect in a percolation model of interconnect failure
The problem of interconnect failure is studied in the framework of percolation theory. The probability failure of a long interconnect due to statistical fluctuations of defects is found. It is demonstrated that two possible diapasons of length to width ratios exist. For extremely long wires, the percolation threshold is determined by rare accumulation of defects, breaking down the wire. For moderately long wires, the threshold concentration of defects is near the macroscopic percolation threshold. The lowering of threshold due to finite width of wire is found. The percolation threshold is found in a two-dimensional system, containing the individual vacancies and voids, caused by coalescence of vacancies.
percolation interconnect failure fluctuations