 can always be written under the following forms: Voth+ Y(E)tox2 a constant of silicon dioxide and a and b two factors, related to the process and to the trapped charge profile, respectively. represent the trapping coefficient and the trapped charge distribution can be asserted from the series development in two limiting cases: when the quantity of traps is small ( <<1): = and =1/3 - for a large quantity of traps ( >>1): =1 and =1/2 3.9.2. SOLUTION FOR NEGATIVE BIAS The current is determined from the boundary condition jp(tox)=0: Like for the positive bias, the trapped charge profile is obtained by integrating the trapping equation, and the voltage shift by a second integration. It yields: with: III-31 This equation can be simplified in two limit cases: when the mean free path is much greater than the oxide thickness (case of a low trap density), or much smaller than it. It yields: When the mean free path is larger than the oxide thickness, i.e. when = developing the exponential term to the third order we find that ( )tends towards tpNTps/6. When the mean free path is smaller than the oxide thickness, i.e. when pNTps>>1, tends towards 1/2. We can summarize the limiting cases in table 6: = tpNTps = tpNTPs (( ) = ( tpNTps //3 ( ) = tpNTps )/6 Table 6. Characteristic coefficients in the case of uniform density of traps. Remark: To come to these reasonably simple analytical solutions, we have assumed that the traps are uniformly distributed across the oxide bulk. This hypothesis is only justified to simplify the calculation. Indeed, expression (47) and fig. 18 show that the trapped charge will have a non- uniform spatial distribution, even if the trap density is uniform. For all practical purposes, the only thing that matters is that the traps be distributed in the oxide bulk (more or less uniformly). This calculation can be made in other cases of interest, such as trapping at one interface. One can define a set of coefficients and for this case. Another solution is to get use of numerical integration, as it is addre