Equivalent Circuit Model for the Gate Leakage Current in Broken Down $\hbox{HfO}_{2}/\hbox{TaN/TiN}$ Gate Stacks

We propose an equivalent circuit model for the post-breakdown (BD) current-voltage (
I
-
V
) characteristics in HfO
₂
/TaN/TiN gate stacks in n-MOSFETs. The model consists of two opposite-biased diodes with series resistances and a shunt leakage path. The circuit admits analytical solution using the Lambert
W
-function and is tested for both negative and positive gate biases in the voltage range of -1.5 to +1.5 V. We also show the versatility of the proposed approach to deal with the post-BD
I
-
V
when source and drain contacts are grounded or floating and analyze the obtained results in terms of the charge available for conduction.