BEOL variability and impact on RC extraction

Abstract

Historically, Back End of Line (BEOL) or interconnect resistance and capacitance have been viewed as parasitic components. They have now become key parameters with significant impact on circuit performance and signal integrity. This paper examines the types of BEOL variations and their impact on RC extraction. The importance of modeling systematic effects in RC extraction is discussed. The need for minimizing the computational error in RC extraction before incorporating random process variations is emphasized.

FastYield: Variation-aware, layout-driven simultaneous binding and module selection for performance yield optimization

“…The standard deviation of the wire length is calculated using (8) where α is a percentage of wire variation. α is found in accordance with the results from [18] as follows 1 :…”

“…In the calculation of T R , we chose to use the sum of the mean and standard deviation since the result corresponds to the required clock frequency for an ~84% yield, for which we target in this study. After a 1 We plotted the equation based on the buffer size vs. wire variation data reported in [18]. …”

Crosstalk analysis in nanometer technologies

“…Note that none of these distributions are Gaussian, since the extraction procedures which transform the physical parameters of interconnect lines to the corresponding electrical parameters are non-linear, and therefore, they tend to result in non-Gaussian distributions for the electrical parameters. This is in contrast with the Gaussian-based assumptions used typically in statistical timing analysis methodologies [12], [16]. The best maximum-likelihood fit for these distributions are lognormal distributions, parameters of which are listed in Table 1 with confidence level of 98%.…”

“…This is in turn due to effects of the neighboring interconnect lines, non-uniform metal densities, NonLinear Resistance (NLR) effect, Selective Process Bias (SPB) [12] effect, and thickness variation due to etching and CMP (Chemical Mechanical Polishing). Other sources of variation are die-to-die, wafer-to-wafer, lot-to-lot, and fab-to-fab variations.…”

“…It is mentioned in [12] that variations in electrical parameters of interconnect may be approximated as normal distributions with the exception of via and contact resistances which should be approximated as lognormal distributions. The Gaussian distribution assumption in this case is found to have and error of 3.5%.…”