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A Three-Dimensional Physical Model for V_{\rm th} Variations Considering the Combined Effect of NBTI and RDF

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2 Author(s)
Panagopoulos, G.D. ; Dept. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA ; Roy, K.

Aggressive transistor scaling affects the threshold voltage Vth in two ways: space and time. Transistors on the same die can have different Vth due to random dopant fluctuations (RDFs). On the other hand, Vth of a specific transistor can randomly shift in time due to random position of dangling bonds and random motion of atomic H or H2 molecules in the oxide [negative bias temperature instability (NBTI)]. These two random effects are not totally independent because the dissociation rate of Si-H bonds at the silicon-oxide interface depends on the nonuniform electric field. In this paper, we describe the combined effect of RDF and NBTI on Vth using stochastic differential equation. In this paper, we are able to examine the effect of RDF on critical NBTI parameters such as kf, kr, and temperature and the correlation among these parameters. The efficacy of the proposed model is evaluated by performing Monte Carlo simulations on various transistors under different direct-current stress and obtained distributions for NIT and Vth.

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Electron Devices, IEEE Transactions on  (Volume:58 ,  Issue: 8 )