4.3 versus

Based on the determination of , , , and , the change of obtained from the measurement-stress-measurement (MSM) routine will now be compared to the change of obtained from the on-the-fly (OTF) method. The results provide valuable information on the applicability of these two measurement routines and furthermore give new insights into the yet not too well known dynamics of the contributing defect states.

Figure 4.12: The OTF1 data, the recoverable component on top of a permanent/slowly relaxing component , their sum , and the pure MSM data evaluated with a delay of are extracted from the left figure as a function of the stress time. The overall degradation of does only qualitatively agree with the OTF1 data points.

By using the universality (cf. Section 4.1) [61, 30], the full degradation of an MSM-stressed device is reconstructed in Fig. 4.11 and Fig. 4.12. Unfortunately, the extrapolated initial values right after stress do not match the degradation gained by the OTF1-method. To explain the differences, the numerical device simulator MINIMOS-NT [89] is used. Applying the drift-diffusion transport model after [90], Boltzmann statistics for the carrier concentrations [10], Shockley–Read–Hall (SRH) interface state dynamics after [91], and mobility variation due to interface state Coulomb scattering [92], a well defined number of defects ( and ) is placed at the interface of a pMOS as used in [17]. The simulated is then post-processed the same way, as already done by the MSM-setup and finally converted to . By using definition (1.1) of , a parametric relationship between and the resulting charge caused by defects is obtained [39]. The occupancy of the interface states determines the detectable charges following the relation , where results in a change of the subthreshold-slope. This finally affects the calculated , as already indicated in Fig. 2.7 and Fig. 2.8.

Simulating the MSM-sequence, shown in Fig. 4.13, yields excellent agreement when mobility changes during stress are neglected. However, many publications have emphasized that mobility variations impact the accuracy of the OTF-method [35, 41]. Simulations performed in [39] showed that an estimated error of in the effective mobility results in a spurious shift in of about ⁴. The error in obtained after an MSM-simulation is roughly for the same device which denotes only a tenth of the simulated -shift. Grasser et al. confirmed these results as being due to the impact of the mobility variation on the extracted threshold-voltage shift. Obviously this impact depends on the applied gate voltage. By employing a numerically simulated -characteristics including a mobility degradation, they showed that the impact of the mobility is largest in the linear OTF-regime and only weak in the subthreshold MSM-regime [39]. Consequently, the determination of should be carried out with safely in the exponential regime of to avoid additional mobility effects.

Figure 4.13: The simulations of the MSM-sequence and OTF-methods based on the measurement sequence depicted in Fig. 4.11 yield sound agreement. The degradation is considered to be due to oxide charges (recoverable part) and interface states (permanent part). The extracted once including (solid) and once not including (dashed) mobility variation confirms that the extraction only slightly depends on the mobility. The maximum error of is observed for . The dotted lines are taken from Fig. 4.11.

When now the measurement sequences depicted in Fig. 4.11 are re-simulated with and without a mobility variation of after stress, as done in [36], Fig. 4.13 is obtained. The extracted perfectly fits to the expected values given by and when mobility changes are neglected, while those including mobility variation yield a constant shift of with respect to the real measurement. This is due to the fact that only interface states are assumed to affect mobility. As these states are considered permanent, only an upwards shift is obtained in the simulation. Moreover, the influence of the MSM-measurement delay, which strongly affects the extracted , is very well described by the simulation results as shown in Fig. 4.14.

Figure 4.14: The simulations of the MSM-sequence and OTF-methods based on the measurement sequence depicted in Fig. 4.11 yield sound agreement. The degradation is considered to be due to oxide charges (recoverable part) and interface states (permanent part). The simulation results as a function of the stress time (lines) with the calculated and components (closed symbols) fit the measurement data (open symbols). Solid lines are with mobility degradation while dashed lines are without. The faster the MSM-sequences are recorded, i.e. the smaller , the more approaches .

A much more complex behavior is observed for the extracted degradation when using OTF methods, since OTF is seriously affected by the shift inherent in the first data point [40]. The larger the delay, the larger the distortion of the overall data gets, resulting in a problem similar to that caused by the MSM time delay, both depicted in Fig. 4.15 and Fig. 4.16. While OTF1 and OTF3 are prone to mobility changes, only OTF2 is uninfluenced by mobility changes. Only when furthermore presuming a of at least small for the latter OTF2, a match of simulation and measurement is achieved.

Figure 4.15: The observed power-law slope as a function of the stress time. The MSM-method does not show severe mobility degradation errors and basically fits better the smaller the measurement delay is.

Figure 4.16: The observed power-law slope as a function of the stress time. Only an extremely fast OTF2 method with a hypothetical initial delay of is able to reproduce the measurement data, while OTF1 and OTF3 are contaminated by , the mobility variation, and compact modeling errors (, etc.).