“…In order to obtain the quantity and distribution of N OX in HK bulk, a new method is proposed, as described in Fig.2, based on PBTI recovery characteristics [12,13]. Figure5(a)shows that the larger trap density of the device with thinner capping TiN under both 90 • C and 160 • C. Figure5(b)shows the energy profile extraction for traps by using ramp recovery stress, which is described in detail below,[14] similar to that in our previous work [15]. (i) V th shift after completing discharge under each V discharge is converted into the effective charge density, i.e., N OX and plotted against V discharge , where N OX = ∆V th ε 0 ε r /dq, with ∆V th = V th (end of each discharge)-V th0 (T stress = 0);(ii) The next task is to convert V discharge into the energy level of E C , i.e., (E T − E C ), by the oxide band structure, the same as that of our previous work,[15] where E T − E C = q •V OX and V g = V OX +V S +V ms , with E T being the trap energy level and E C the conduction band of substrate silicon, and V S the surface potential drop;…”