Two-step probability plot for parameter estimation of lifetime distribution affected by defect clustering in time-dependent dielectric breakdown

Abstract

In this study, a simple method of statistical parameter estimation is proposed for lifetime distribution that has three parameters due to the defect clustering in the middle-of-line and back-end-of-line. A two-step procedure provides the estimations of distribution parameters effectively for the time-dependent dielectric breakdown. In the first step, a clustering parameter of distribution, which is one of the shape parameters, is estimated by a linearization treatment of plotted data on the proposed chart. Then, in the second step, shape and scale parameters are estimated by calculating of a slope and an intercept, respectively. The statistical accuracy of the estimates is evaluated using the Monte-Carlo simulation technique and mean squared error of estimates.

Statistical evaluation method for lifetime distribution in field-accelerated time-dependent dielectric breakdown using two-step probability plot and multilink test scheme

“…Recently, the statistical probability plot for GBXII distribution has been proposed and evaluated for its parameter estimation accuracy. 27,28) Equation (1) can be converted to…”

“…27,28) The two-step probability plot is used to easily obtain the parameters of GBXII distribution by using a solver tool and a specific plot as follows. STEP 1: Let α be the estimated value that maximizes the correlation coefficient (≤1) between log½RðtÞ À1= À 1 and log t with a solver.…”

“…3,4,[25][26][27][28][29] The model has two shape parameters and is called the generalized Burr-type XII (GBXII) distribution in statistics. 30,31) The cumulative probability function of the lifetime distribution with defect clustering is described by the BXII distribution as…”

“…A two-step probability plot 27,28) and Monte Carlo simulation (MCS) will be used for the study of statistical estimation accuracy. Merits of the multilink test and a combination effect will be discussed on the basis of statistical accuracy.…”

“…A complicated shape of the TDDB lifetime distribution 3,4,[25][26][27][28][29] is represented by both the intrinsic variation of TDDB and the physical variation of acceleration stress. Therefore, large-scale observation of lifetime is required for evaluating the lifetime distribution of TDDB affected by the clustering defect.…”