e present formulation is that of the CEA team (coefficients a= .Nt, Y and ft functions, F functions cf. [Lera-89a], [Pail-99] and this chapter). All these formulations proceed from the same spirit. Authors have widened this formulation to interface states (cf. hereafter) [Flee-92, Berl-92], but physical basis are not SO firm as for charge trapping (coefficients fot, fit). Anyway the major drawback of these schemes is to skip all the physics involved in the kinetics of charge build-up and detrapping. But they are instrumental as a first-order approach. 3.13.2. NUMBER OF TRAPS NT AS A KEY PARAMETER When at sufficiently high dose, all traps are filled, and saturation is reached. Charge density is then in the case of interface trapping: (72) Qot=N III-43 and therefore the saturation value of the threshold voltage shift is (under the simplifying assumptions): Vot.sat =-ANttox with Volts / charges.cm According to this model, the parameter N is present at low doses and large doses (fig. 28). It is therefore this parameter that one must reduce. This generally implies the modification of the manufacturing process. THRESHOLD VOLTAGE SHIFT THE NUMBER OF TRAPS Slope : Proportional to a = 0 Saturation Voltage : SATURATION REGION LINEAR REGION => TECHNOLOGY HARDENING Nt = f(process) 0 100 1000 Dose (krod) Figure 28. Separation of Vot threshold voltage component at low and high dose under simplifying assumptions We note that this simple formula is linear as a function of dose (Volt/kilorad) and quadratic as compared to the oxide thickness. It applies only at low to moderate dose (e.g. some kilorads or hundred kilorad) and depends substantially on manufacturing process and oxide thickmess. Beyond this limit, the response is governed by a more complex exponential relationship or can't be understood without numerical integration of the set of differential equations, with the correct parameters. 3.14. EXTRACTION OF TRAP PARAMETERS Once we have determined the trapping behavior of a particular oxide by means of the techniques present