TABLE OF CONTENTS In equilibrium, the probability of occupancy of interface traps is given by the Fermi-Dirac distribution function which gives the probability of a given energy state being occupied by an electron,
where E t is the energy level of the interface trap and E F is the Fermi energy level (Fig. G.1). The probability of occupation of an energy state at the Fermi level energy is one-half.
Defining the potential of the interface trap with respect to the intrinsic energy level E is at the surface as
the Fermi-Dirac distribution becomes
where the variable u represents the potentials normalized to the thermal voltage. Out of equilibrium the occupancy of the interface traps is given by the Hall-Shockley-Read statistics (see Appendix F), according to expression (F.11), which is simplified to
for equal capture cross-sections of electrons and holes. For a p-type semiconductor, the electron and hole densities are given by (2.4.9) and (2.4.10) repeated below
At the surface of the semiconductor, u=u s; thus, the substitution of (G.5) and (G.6) into (G.4) yields
which can be written as
A detailed analysis of (G.8) is presented in [2], where it has been shown that for small channel voltages and high inversion level,
Therefore, (G.9) reduces to
where we have written f FD instead of f HSR. In effect, (G.10) is similar to (G.3) with u F +u C in the...
