Quantum mechanical modeling of charge trapping/detrapping phenomena in CMOS devices with high-k stack gate dielectrics

Abstract

Electrical instability is one of the major concerns regarding high-K-based field-effect transistors (FETs); threshold-voltage (VT) shifts observed in pulsed measurements is considered to originate from the tunneling of channel electrons into traps in the gate dielectrics. Although some experimental models done by previous researcher are useful for providing qualitative explanations, a device-level numerical model is nonetheless necessary to quantitatively analyze the origin and impact of the electrical instability in such multi stack systems. The charge trapping/detrapping model to analyze the gate threshold voltage instability reported so far have been using detrapping of the trapped charges back to the channel alone ignoring the detrapping to the gate. But a complete quantum mechanical is necessary to observe the behavior of charge trapping and threshold voltage instability. In this context, a quantum mechanical model (QM) is presented for analyzing the threshold voltage instability induced by charge trapping/detrapping for the inversion gate capacitance of MaS structures with high-k gate dielectrics. The threshold voltage shifts are modeled based on a modified rate equation and the properties of carriers in inversion layers are studied by solving coupled SchrOdinger's and Poisson's equation self consistently. The model incorporates the effects due to detrapping of charges to the gate region which has been taken as negligible before. The accuracy of the model has been verified with some reported experimental results. It is evident from the results that, not only the further shrinking of Effective Oxide Thickness (EaT) but also increasing gate pulse width influence the detrapped charges that play a significant role in the threshold voltage instability. And these detrapped charges to the gate region also increase the gate current of the MaS devices, which is under estimated if calculated without considering these charges.