Results

9.3 Results

To validate the multi-state defect model described in the last section, experimental data with logarithmically increasing stress times for different temperatures $T$ and stress voltages $Vstr$ is essential. This measurement data is then fitted by using a single parameter set. Eventually, the calibrated parameter set is shown in the following to successfully account for all performed measurements.

Figure 9.9: The relaxation sequences of an measurement-sequence with logarithmically increasing stress times are plotted versus the simulation results. The same calibrated parameter set of Chapter 9.2.1 is applied for all simulations, yielding sound agreement.

For a given temperature and voltage, as illustrated in Fig. 9.9, it is possible to simulate a complex eMSM-sequence, consisting of logarithmically increasing stress times, with very good agreement. Furthermore, the last relaxation sequence after more than $2000s$ of stress is compared at different temperatures and for different stress voltages, cf. Fig. 9.10. Despite device to device deviations, as various MOSFETs have to be used for the measurements to avoid pre-stress, it can be clearly seen that the measurements are very well reproduced using the multi-state defect model in combination with a broad defect distribution.

Figure 9.10: The last relaxation sequence is depicted for different temperatures (top) and stress voltages (bottom). It can be clearly seen that the measurement is very well reproduced using the multi-state defect model.

It was already mentioned that an investigation of the time dependence of a single defect is not reasonable in large device. However, the relaxation behavior observed in Fig. 9.9 and Fig. 9.10 can be modeled by the superposition of defects with different emission time constants. This is confirmed by Fig. 9.6, where the percentage of the charged oxide defects is correlated with the last relaxation sequence for $∘ 125 C$ and $Vstr = 1.83V$ . At the beginning of the relaxation $9%$ of the possible defects contribute, while after about $400s$ relaxation only $1%$ are left, which is equivalent to nearly complete relaxation of the switching traps. The permanent part left can be explained by recalling the two-stage model [98], which assumes depassivated interface states contributing to the permanent part of NBTI (Fig. 9.10). In the simulation the permanent part was modeled by an additional defect level which can only be filled during stress. During recovery the defect level remains occupied.

A further issue when dealing with device simulations was the already mentioned exactness of the distributions due to the different amount of taken defects. Here a number of 1000 representative defects exhibits a good compromise between computational efforts and accuracy of the simulation when fitting the experiments. Therefore this value is chosen for the calibration of the parameter set. When taking more defects into account, the simulation results become smoother and do not contain the small kinks, as visible in Fig. 9.10 for 1000 defects. However, this is only due to numerical reasons, since the actual degradation is always obtained by scaling the behavior of the “respresentative” defects. Consequently, the overall behavior is not changed, which can be seen when comparing Fig. 9.10 and Fig. 9.11.

Figure 9.11: The last relaxation sequence as depicted in Fig. 9.9 for different temperatures and stress voltages. When using 10000 instead of 1000 defects the simulation results become smoother. Although the simulation was performed with the same parameter set, the measurement is quite well reproduced.

At last, it can be pointed out that the classical approach, which assumes all holes to be energetically located at the valence band edge of the substrate, shows small deviations from the QM-results, especially for $125∘C$ and $Vstr = − 1.83V$ , cf. Fig. 9.12. This is due to the missing influence of the subbands which are localized in the SiGe-layer.

Figure 9.12: The last relaxation sequence as depicted in Fig. 9.9 for different temperatures and stress voltages. The classical results assume all holes to be energetically located at the valence band edge of the substrate. Except for the heaviest stress conditions ( $125∘C$ and $Vstr = − 1.705V, − 1.83V$ ) the classical approach can as well be applied and yields rather good agreement with the experiment.

[next] [prev] [prev-tail] [front] [up]