Analyzing the distribution of threshold voltage degradation in nanoscale transistors by using reaction-diffusion and percolation theory

作者：Islam Ahmad Ehteshamul^*; Alam Muhammad Ashraful

来源：Journal of Computational Electronics, 2011, 10(4): 341-351.

DOI：10.1007/s10825-011-0369-4

• Reaction-diffusion model
• Markov Chain Monte-Carlo
• Interface defect statistics
• Skew-normal distribution
• Exponential distribution
• Threshold voltage degradation

Continued scaling of transistors into the nanoscale regime has led to large device-to-device variation in transistor characteristics. These variations reflect differences in substrate doping, channel length, interface and/or oxide defects, etc. among various transistors. In this paper, we develop a theory for the statistical distribution of threshold voltage degradation (Delta VT) due to the Negative Bias Temperature Instability (NBTI). First, we model the time dynamics of interface defects within the Reaction-Diffusion (R-D) framework and calculate the statistics of interface defect using Markov Chain Monte-Carlo method. We show that the generation and annealing of interface defects are strongly correlated and that the statistics of interface defect at a given stress time (N-IT@t(STS)) follows a skew-normal distribution. Second, we explore the differential effect of the spatial distribution of interface defects in nanoscale transistors pre-populated with a discrete number of randomly placed substrate dopants. We model the effect of spatial distribution of defects using a percolative network and demonstrate that the distribution of threshold voltage degradation for a single additional interface defect, i.e., Delta V-T@ Delta N-IT = 1, is exponential, with a fraction of transistors having Delta V-T similar to 0. Finally, we obtain the statistics of Delta V-T@t(STS) by convolving the statistics of N-IT@t(STS) with that of Delta V-T@similar to N-IT = 1. The resultant statistics of Delta V-T@t(STS) compares favorably with a broad range of experiments reported in the NBTI literature.

• 出版日期2011-12