4.2.3 Impact of Pre-stressed Interface State Density Profile on HCD Modeling

**Figure 4.9:** (a) Interface state density profile evolution calculated with developed HCD model under assumption of a uniform initial profile and employing N_it(x) extracted according to the proposed scheme. (b) Comparison of the I_dlin degradation calculated with MiniMOS-NT using obtained N_it(x) profiles (a) as input degradation characteristics.
(a) (b)

The information on the initial interface state profile is significant in the context of hot-carrier degradation modeling. The impact of the initial N_it distribution on the degraded device characteristics within the developed physics-based model of HCD (see Section 3.1) is examined. The proposed approach considers the interplay between the single- and multiple-carrier mechanisms of Si-H bond-breakage. The bond is interpreted as a truncated harmonic oscillator with the corresponding ladder of eigenstates. All oscillator transitions are considered within a system of rate equations. The solution of the system relies on the initial conditions, that is the initial concentration of the virgin Si-H bonds. If some of these bonds are already pre-broken, the density of bonds available to be ruptured is reduced. Therefore, the pre-existing dangling bonds already impact the characteristics of the fresh device which differ from those typical for an ideal transistor (with pre-stressed N_it = 0) of the same configuration. Due to this initial interface state density profile the solution of the rate equation system - i.e. N_it(x,t) - is modified.

Figure 4.9a (obtained for stress V_ds = 5.0V and V_gs = 2.0V) illustrates this tendency, showing the evolution of the interface state profile with stress time, calculated by considering the uniform and the nonuniform initial N_it distributions. The lack of details obtained from the uniform N_it approach is apparent. It can be seen that the difference is more pronounced at short stress times because at longer times the total N_it is already rather high, thereby screening the impact of the pre-stressed N_it dose. This tendency is confirmed by Figure 4.9b which demonstrates that the linear drain current change (calculated using real and uniform N_it(x,t) profiles) is significantly modified for stress times shorter than 10²s. This trend means that an initial interface trap density can affect the device behavior only in the case of short stress times and relatively weak stresses. The second demand corresponds only to the case of real device operating conditions when the applied voltages are relatively low, compared to accelerated hot-carrier stresses.