Since the McWhorter model suffers from a weak temperature dependence of and small time constants, Kirton and Uren [56] incorporated field-independent barriers in the cross sections and (see Section 2.5). The ‘ad hoc’ introduction of these barriers has been motivated by the theory of nonradiative multi-phonon transitions (NMP) process [115]. However, Kirton and Uren have not provided a detailed theoretical derivation based on this NMP theory. Nevertheless, their work is regarded as a substantial improvement in the interpretation of charge trapping at semiconductor-oxide interfaces and thus also referred to as the standard model throughout this thesis. In an extended version of the McWhorter model, the holes can also be captured by traps with an energy below the substrate valence band. As illustrated in Fig. 2.5 of Section 2.5.2, the required barriers consist of two components, namely and . The latter is the required minimum energy for a hole capture process while is the barrier component which must be overcome for hole capture as well as emission. In this variant, the capture and emission time constants read

where the traps are not restricted to lie within the bandgap. Its behavior with respect to the temperature and the oxide field is illustrated in Fig. 6.1 and evaluated based on the TDDS checklist in Table 6.1. When the trap level lies below the valence band edge (), shows an exponential field dependence, which is superimposed by a sharp peak due to a drop of the hole concentration at weak oxide fields. Comparing the model to the experimental TDDS data (see Section 1.3.4), this exponential behavior allows for reasonable and approximative fits to but it is incompatible with the observed curvature in . Furthermore, the model predicts to be field insensitive for according to the equations (6.4). It should be mentioned at this point that the derivation of the analytical expression (6.3) and (6.4) is based on Boltzmann statistics, leading to small deviations in and compared to the simulations of Fig. 6.1 (left) using Fermi-Dirac statistics. The weak field dependence of the simulated reasonably agrees with the behavior of ‘normal’ (constant emission times) but is inconsistent with as well as ‘anomalous’ traps (a drop at weak oxide fields). Nevertheless, Fig. 6.1 reveals that the introduction of yields the required temperature activation and larger time constants in agreement with the points (ii) and (v) of the TDDS findings.A fit of the Kirton model to the experimental TDDS data is presented in Fig. 6.2. Although the model can reproduce some features seen in the TDDS data, except for the curvature in , no reasonable agreement with the measurement data could be achieved. This discrepancy can be explained as follows: The exponential bias dependence extends up to a voltage at which coincides with . In Fig. 6.2 (left) is approximately so that shows an exponential bias dependence up to this value and becomes constant afterwards. Therefore, must be chosen such that lies above the voltage range used in the measurements. This is only the case for defects whose trap levels are situated sufficiently low. Note that those defects are also characterized by a large , which marks the voltage where coincides with . After equation (2.66), their must equal their at , visible as the crossings between and in Fig. 6.2. At a low gate bias, their trap levels are moved far below so that their emission times fall several orders of magnitude below their corresponding capture time constants. The large difference between and predicted by the Kirton model is inconsistent with the experimental TDDS data. Additionally, a fit of the Kirton model to is presented in Fig. 6.1 (right). It clearly shows that the simulated fails to reproduce the experimentally obtained when a good match with is achieved.