Physical Basis of Lognormals in Reliability for Microelectronics With Deposited Metal Layers

Lognormal Probability Density Functions (pdfs) are often empirically found to fit the distribution of failure lifetimes for electronic components, but prior to this work, a physical basis has not be found for why Lognormals should be applicable. Using long-thin metal interconnects atop non-conducting substrates as a representative system, we show Lognormals pdfs for device lifetimes naturally arise, whenever there is a standard Gaussian variation in device geometry, with the case studied being variations in metal interconnect line-widths.