20 Dandling Bonds Interface States Figure 10. Classification of charges [Deal-80]. Since then, finer studies have shown that reality is not as clear. It seems likely that there exist sites in the volume close to the interface that exchange charge with the surface of the silicon [Fleet-92], in a reversible manner as for states, but much more slowly (these slow states are called "border traps" or "switching states"). There also exist time-evolving phenomena that are identified by the (irreversible) neutralization of charge in the volume close to the interface. In what follows, we develop simple statements without describing the "border traps" concepts. Restrained to the charges that do not exchange reversibly with silicon, the global formula for threshold voltage shift here becomes: .|p,(x)-n,(x)+p(x)-n(x)|d> where V ot is the oxide-trapped charge, and nt and Pt are the oxide-trapped electron and hole densities of charge (in units charge.cm-3. The exact trap profile is most of the time unknown. It is therefore convenient to define an integral of this density rather than the profile itself. One can define Qe and Qh (more simply Qe and Qh when no ambiguity occurs), as: To more easily allow reasoning on trapped charge profile, two useful additional quantities can be III-14 defined to represent the charge distribution by its first moment, i.e. the location of charge centroids in the oxide: where is the total charge present (except the interface and border traps), and: (10) X. is the projected total charge (note that all the quantities Q are surface densities of charges expressed in unit "number of charges per unit area"). Therefore, one can write a simple expression of the voltage shift, each term with a different signification: The free carrier density, as will be computed numerically in next sections, is insignificant in long-lasting natural irradiations (n and p are between 106 and 106 carriers.cm-3 for dose rates ranging between 10-3 and 103 rad.s-1.) It is of course not the case for trapped charges as they accumul