The expression of current jp at the interface is obtained by solving the continuity equation for free holes in the stationary regime. By neglecting the diffusion term and in the case of quasi-uniform electric fields, the current gradient is simply and since p==in the stationary regime, we get: which yields: (62) = III-33 which corresponds to the hole collection function at the interface. For strong fields, fh (E) 1. For low fields, In the same manner, we can calculate the expression of the electron current at the interface for VG positive by solving the continuity equation for free electrons in the stationary regime. For this purpose, let us introduce the actual extension of the hole trap distribution, and let us assume this extension is small before tox. Be Xh the centroid of the trapped holes (small with respect to tox). We obtain: where fe (E) corresponds to the electron collection function at the interface. As electrons are much more mobile than holes, expression of fe should gather several components: The drift component, calculated for holes. However, that as we can assume that fe 1 Other mechanisms not described here, such as diffusion, hot electrons. (Extension could be made to electron injection from silicon, not addressed here). We proposed to lump these terms, into two terms representing diffusion and LH/tox representing possible hot-electron component. We can therefore solve the evolution equation for charged traps at the Si/SiO2 interface by replacing the currents by their expressions. It becomes: (65) ( where The voltage shift associated with this charge trapped at the interface can be written [Lera-89a]: (67) ani It is possible to separate the behaviors at low and high dose by developing the exponential term in linear and in saturation parts. It yields: III-34 - at low doses, Vot h f,(E)Y(E) tox' 2 D - at high doses, - A 1 +F(E) NTPS tox A=9==4.76 q = Volts / KA / 10 1 12 charges.cm-², -2 , being introduced as another characteristic constant of SiO2. III-35 3.11. ANALYTICAL MODELING Eqn. 68 and 69 