Monte Carlo evidence for need of improved percolation model for non-weibullian degradation in high-κ dielectrics

Dielectric breakdown is one of the critical failure mechanisms and showstopper for ultra-large scale integrated (ULSI) circuits as it impacts the performance and functioning of the transistor, which is the fundamental unit governing the operation of all the advanced microprocessors that we have today. As a reliability engineer, it is essential that the failure mode and mechanism be best described using statistical distributions that correlate with the physical mechanism and driving forces causing failure. In many cases, the distributions used to represent the time to failure data are empirically assumed, without carefully considering its implications on the extrapolated predictions of field lifetime. Application of a wrong distribution can give lifetime estimates that vary by many orders of magnitude, which nullify the very purpose of the reliability study in itself. The Weibull distribution is commonly used to describe random defect generation induced percolation failure of the oxide (dielectric) by means of the “weakest link” phenomenology [1, 2]. While the assumption of a Weibull distribution is well justified for silicon oxide (SiO₂) and silicon oxynitride (SiON) materials [3, 4], the application of the same stochastics for high permittivity (high-κ) dielectrics is questionable [5] - [7]. This is fundamentally attributable to the different microstructure of the grown / deposited dielectrics, which we will discuss in detail, along with strong physical analysis evidence. We will present further evidence using Kinetic Monte Carlo (KMC) simulations to explain the origin of the non-Weibullian trends observed. The key motivation of this study is to caution microelectronics reliability scientists against the use of standard statistical distributions for all scenarios. We may have to resort to the need for non-standard distributions or selectively use the standard distributions only over confined percentile ranges, as material and dev- ce failure mechanisms become increasingly complex and interdependent in nanoscale integrated circuits.