ped carriers 3.7.4. Equation relative to the electric field 3.7.5. Equations relative to the currents Solution for the steady-state case of irradiation: Mean free paths for holes and electrons. Limiting cases Case of a single type of trap 3.9.1. Solution for positive bias 3.9.2. Solution for negative bias 3.10. Low dose and high dose regimes in the simplifying case of interface trapping 3.11. Analytical modeling 3.12. Practical applications 3.12.1. Electrical measurement techniques 3.12.2. Behavior in the low dose regime III-1 3.12.3. Case of charge trapping at the SiO2/Si interface 3.12.4. Case of charge trapping in the bulk of the oxide 3.12.5. Case of a multilayer insulator 3.12.6. Behavior in the high dose regime 3.13. Simple method to evaluate the hardness factor of a MOS process for the trapping of holes 3.13.1. Simplified formula 3.13.2. Number of traps Nt as a key parameter 3.14. Extraction of trap parameters 3.15. Case where two type of traps are present 3.15.1. Case of uniform distribution of traps 3.15.2. Case of interfacial distribution of traps NUMERICAL MODELING OF TRAPPING Background Simplified Numerical 1D on laptop computer: the TRAPPOX" R v.4 code and various applications 4.2.1. V-Model 4.2.2. J-Model 4.2.3. Trends in modeling 4.2.4. Method used in TRAPPOXR v.4 and code implementation 4.2.5. The effects of gate bias: the cases of trapping in volume and at interface Case of an unhardened power MOS transistor. The field collapse effect 4.4.1. Consequences in the case of an irradiation under positive gate bias 4.4.2. Consequences in the case of an irradiation under negative gate bias 4.4.3. Conclusions 4.4.4. Numerical illustrations using three different codes Gate bias switching DETRAPPING AND TIME-EVOLVING EFFECTS Annealing, reverse-annealing and rebound Modeling the trapping and thermal detrapping effects 5.2.1. Modeling PIE in terms of energy spectra: principles and equations 5.2.2. Results TRAPPING AND LINKS WITH THE MANUFACTURING PROCESS Defects Some views on response of thermal oxides modeli