p are the diffusion coefficients for electrons and for holes, which verify the Einstein relationship recalled below: with peff=pexp(-E;/kT) (cf. Eqn. 21). The expressions of currents Jn and jp can be inserted into the preceding equations. The four continuity equations for free carriers and trapped charges, coupled with the equation of the internal electric field, constitute the system that allows us to calculate the profiles of the charge trapped in the oxide. The voltage shifts associated with charge trapping in the oxide can then be deduced by integration. Without any further simplifying hypothesis, this system of five coupled equations can only be solved numerically. In the following, we shall make simplifying assumptions to derive usable analytical expressions. SOLUTION FOR THE STEADY-STATE CASE OF IRRADIATION: MEAN FREE PATHS FOR HOLES AND ELECTRONS. LIMITING CASES Instead of trying to solve numerically this system of five coupled equations, we can attempt to find some simple analytical solutions corresponding to typical profiles of trapped charges. These analytical resolutions are valid as long as the generation of free carriers remains little disturbed by the trapped charge, i.e. when the space charge effect is not too important. They are therefore limited to low doses of irradiation, and need simplifying hypotheses. III-26 The first simplifying assumption is that corresponding to the stationary regime. The method [Lera-89a, Lee-91, Kran-87] then basically consists in solving the continuity equations for free carriers, by assuming that n/ t = p/ t = 0. We assume that the radiation-induced free carriers do not accumulate in the oxide, and thus are either trapped, or swept away at the electrodes. SiO 2 n>>tox p<<tox Figure 17. Illustration of the electron and hole currents in the oxide (for a constant dose rate), under positive gate bias. In the following, let us examine the case of an irradiation under a positive gate bias. The case of a negative bias will be deduced by symmetry. The boundary conditions for