Modeling of NBTI Induced Threshold Voltage Shift Based on Activation Energy Maps Under Consideration of Variability

One of the major challenges for modeling BTI degradation in modern technology nodes and deeply scaled transistors is the occurrence of significant time dependent variability (TDV). This means that due to the sparsity of defects, the impact of single defects as well as variation in the number of defects per device need to be taken into consideration. We present a modeling approach based on physical principles to describe both mean parameter degradation as well as TDV. Our approach is based on activation energy maps combined with an exponential-Poisson model in order to capture variability. For parameter extraction a combination of ultra fast measurements on large area transistors and transistor array measurements are applied. Thereby, ultra fast measurements have the capability to make a wide range of capture-/emission times experimentally accessible, improving the confidence of the extracted activation energy map. On the other hand, transistor arrays have proven to be the ideal test vehicle to efficiently measure an ensemble of transistors and to asses TDV.