Moisture absorption impact on Cu alloy/low-k reliability during process queue time

The impact of process fluctuations for the lifetime distribution of middle-of-line time-dependent dielectric breakdown was investigated by Monte-Carlo simulation. Global and local variations were simulated using a doubly truncated normal distribution. A goodness of fit to the generated data was determined statistically in terms of the Weibull distribution and clustering model. A change in the standard deviation of the global variation shows a large contribution to lifetime variation. However, it does not affect the average lifetime. A change in the standard deviation of the local variation contributes to both the average lifetime and the distribution variation. The upper limit of the process variation induces the convex upward shape of the lifetime distribution on the Weibull plot. The clustering model well explains the distribution shape.

Section: Monte-carlo Simulationmentioning

confidence: 99%

Simulation study for lifetime distribution of middle-of-line time-dependent dielectric breakdown affected by global and local spacing variations

Yokogawa¹

2016

“…13) However, the spacing variations of contact-to-gate or via-to-line spacing remarkably affect the TDDB lifetime at the middle-of-line (MOL) and backend-of-line (BEOL) owing to electric field acceleration. [14][15][16][17] Hence, the Weibull distribution often cannot describe the spacing variation impacts on lifetime distribution. 4,[18][19][20][21][22][23][24][25][26] One of the lifetime distribution functions, which is based on the defect clustering concept, describes the spacing variation impacts well.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference of a lifetime distribution parameter on the time-dependent dielectric breakdown with clustering defects

Kunii

Endo

Yokogawa

2019

In this study, we compared three statistical methods including the Bayesian inference to evaluate the lifetime distribution of time-dependent dielectric breakdown with clustered defects. Especially, we focused on the effect of the prior information of the Bayesian inference to obtain an accurate low cumulative failure probability of lifetime distribution. The prior information about the breakdown physics can give an appropriate range of shape parameter of the distribution function. In comparison with the conventional estimation methods, we investigated the influence of sample size and prior distribution on parameter estimation accuracy of the Bayesian inference.

“…The Weibull distribution tended to fit the observed lifetime data of time-dependent dielectric breakdown (TDDB) extremely well. 8) However, the spacing variations of contact-to-gate or via-to-line spacing remarkably affect the TDDB lifetime at the middle-of-line (MOL) and backend-of-line (BEOL) owing to electric field acceleration, [8][9][10][11][12] and the Weibull distribution often cannot describe the spacing variation impacts. 4,[13][14][15][16][17][18][19][20][21] A lifetime distribution function, which is based on the defect clustering concept, well describes the spacing variation impacts.…”

Section: Introductionmentioning

confidence: 99%

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

Yokogawa

2017

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.