Generalized trapping kinetic model for the oxide degradation after Fowler–Nordheim uniform gate stress

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Abstract
The practicality of modeling the power law degradation observed in thin dielectrics after Fowler–Nordheim stress has been demonstrated on the basis of a generalized trapping approach with appropriate trap cross-section and density profiles. A detailed mathematical analysis of the negative bulk oxide charge kinetics has been established using incomplete Gamma and generalized hypergeometric functions, after assuming exponentially varying trap cross-section and density profiles throughout the oxide. These spatial distributions could be due to the structural nature of the oxide after growth. Moreover, the asymmetry of the charge distribution centroid for negative and positive gate bias stress has been satisfactorily interpreted by neglecting the trapping in the tunneling region near the cathode. Overall this generalized kinetic trapping model provides very good fitting of the variation of the trapped oxide charge with the injection dose for oxide thicknesses between 5.5 and 10 nm. The evolution of the charge centroid is also well predicted but with less accuracy, due to the presence of other concurrent charge generation processes associated with positive and/or negative charge buildup.