Prediction of dielectric reliability from I–V characteristics: Poole–Frenkel conduction mechanism leading to √E model for silicon nitride MIM capacitor

Reliability of gate dielectrics and metal–insulator–metal capacitors

“…For area and perimeter extrapolations also a structure with the largest area should be integrated. Usually, areas range from a few lm 2 to nearly 1 cm 2 [42].…”

“…A sqrt(E)-model has been reported for a nitride MIM-capacitor dielectric [33,42] and for tantalum pentoxide dielectric [34]. Fig.…”

Design techniques to improve time dependent dielectric breakdown based failure for CMOS circuits

“…where E f is the electric field like the previous two models, and Q BD is the critical charge or the breakdown charge, Φ B is the trap depth, q is the elementary charge, ε 0 is permeability in a vacuum, and ε∞ is permeability in the dielectric [9]. Again, the square root E dependence can be seen.…”

“…There are at least five (5) oxide breakdown models currently used by reliability engineers: the Bandgap Ionization Model, the Classic Anode Hole Injection (1/E) Model, the Hydrogen Release Model, the Thermochemical (E) Model [8], and a combination of the Charge-to-Breakdown (QBD) Hypothesis and the Poole-Frenkel (PF) Conduction (√E) Mechanism [9]. The important models to consider are the Classic Anode Hole…”

“…The charge to breakdown hypothesis states that once a critical charge has been forced through the dielectric, the dielectric will break down. Also, the Poole-Frenkel Leakage Mechanism predicts that leakage current interacts with the dielectric which leads to degradation [9]. The corresponding equation…”