5.7 Simulation of the Charge Pumping Current

To approximately account for the above mentioned temperature and field activated tunneling process, a modified Shockley-Read-Hall (SRH) model⁴ is used within our device simulator Minimos-NT [89]. The SRH-capture-rates are multiplied by

(5.2)

where is the electric field in the oxide, is a reference value, the multi-phonon emission barrier and the thermal energy. can be characterized by a Gaussian distribution with the mean energy . When setting the parameters some points need to be considered in order to end up with a physically appropriate model:

1. The first exponential factor in (5.2) models the bias dependence. It is very sensitive to changes of due to the squared exponent, leading to a very small range of valid values. This reference field acts as a scaling factor.
2. When setting the barrier too low, the oxide traps contribute to the interface trap signal as the second factor approaches unity. Setting the barrier too high leads to very low rates, effectively eliminating the contribution of oxide traps.
3. The distribution of determines the dependence of on . Increasing the mean of the distribution at increases the mean capture/emission-time constants. Since with constant-slope pulses higher pulse amplitudes require longer pulse durations, increasing the mean shifts the point from which a significant contribution of oxide traps can be observed to higher pulse amplitudes. On the other hand, broadening the distribution of (increasing the variance) also broadens the distribution of time constants, observable as broadening the range of where increases.
4. Lastly, the distribution determines how strong some oxide traps contribute to the -signal in each time-interval of the pulse. To achieve a smooth quadratic behavior as observed in the experiments, Fig. 5.18, a broad Gaussian peak over a wide range of energies is required (), consistent with other NBTI experiments [98, 100].

The final simulation results are depicted in Fig. 5.18. As the simulation treats the CP measurement process as stress-free, no additional interface traps are created and only the oxide-charge part is visible. With the thermally activated barrier the increasing can be described.

Figure 5.18: The contribution due to oxide traps can be well described using the model suggested in [98]. This model assumes that hole-trapping is possible via a multi-phonon process implying a thermally activated barrier and an field dependence. It is stipulated that the simulation only describes oxide traps and interface traps without applied stress conditions. Additional interface traps due to NBTI stress are missing in the simulation because of a constant number of interface traps for each simulation point (solid circles).