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A semi-empirical analytic model for threshold voltage instability in MOSFETs with high-k gate stacks

A semi-empirical analytic model for the threshold voltage instability of a MOSFET is derived from Shockley–Read–Hall (SRH) statistics to account for the transient charging effects in a MOSFET high-k gate stack. Starting from the single energy level and single trap assumption, an analytical expression for the filled trap density in terms of dynamic time is derived from SRH statistics. The semi-empirical analytic model for the threshold voltage instability is developed based on MOSFET device physics between the threshold voltage and the induced trap density. The obtained model is also verified by extensive experimental data of trapping and de-trapping stress from different high-k gate configurations.