TBD (a) and QBD (b) versus gate voltages in the log-log scale for 2.15 nm oxides stressed in substrate injection mode using p+poly/SiO2/n-Si capacitors of 10−4cm2 at various temperatures.
(a) Non-Arrhenius temperature dependence (280 °C − 30 °C) of TBD and QBD for high-κ/SiO2 bilayers of pFETs of 0.006 mm2 stressed in inversion mode with W/L = 0.15 mm/0.04 mm. Higher ΔH of TBD is due to the temperature dependence of the gate leakage current. (b) Comparison of the non-Arrhenius QBD temperature dependence ( ∼200 °C to −50 °C) of high-κ/SiO2 bilayer pFETs and SiO2 dielectrics (2.69 nm) under substrate injection.
Schematic picture of the defect generation process in electron energy-based breakdown models. Electrons are injected through the oxide and partially loose their energy at the anode interface to release some positively charged species (holes or protons) with an efficiency ζ1. On the other hand, ζ2 represents the probability of the released species to create defects by reaction with bulk precursors and ζ3 the probability of loosing the generated species towards the electrodes.
Schematics of the thermally assisted hydrogen release model. When Si-H bond is in the ground state at T = 0 °C (a), Si-H breakage occurs through excitation over all the energy-levels by electrons. When Si-H bond is excited to higher energy states at finite temperatures (b), the number of energy levels for bond breakage are reduced, leading to smaller exponents since the power-law exponents is equal to 4N. 9–12 This new model explains the reduction of the power law exponent with increasing temperature.
Comparison of the thermally assisted hydrogen release-reaction model with experimental data (symbols) for 2.69 nm heavily nitrided oxides from 200 °C to −50 °C. The model results (lines) of α = 1.8 and A = 6 × 10−4 are normalized to the QBD data at 170 °C. The modelling results of all other cases are normalized at −50 °C for clarity of the comparison.
Comparison of the contributions of release-only and reaction-only with the complete hydrogen release-reaction model and with experimental. This illustrates that both processes are required to explain the full range of experimental data (Fig. 6 ) whereas non-Arrhenius temperature dependence arises only from the temperature dependence of hydrogen release process.
Comparison of the thermally assisted hydrogen release-reaction model (lines) with QBD data (symbols). (a) 2.67 nm SiO2 under substrate injection (+VG) using p+poly/SiO2/n-substrate capacitors (b) 2.23 nm SiO2 under gate injection (−VG) using n+poly/SiO2/p-substrate capacitors. In both cases, the area is 10−4cm2.
The contributions of high and low energy levels of vibrational excitations for hydrogen release at high- and low-temperatures in comparison with QBD data from Fig. 1(b) .
Comparison of the thermally assisted hydrogen release-reaction model (lines) with the experimental QBD data (symbols) of high-κ/SiO2 bilayers in pFETs stressed under inversion mode using an area of 0.006 mm2 with W/L = 0.15 mm/0.04 mm: (a) Comparison of non-Arrhenius temperature dependence at a fixed VG of −2.8 V and (b) comparison at different voltages and temperatures. Normalization of the model is made at −2.8 V and 170 °C.
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