3.4 Temperature and oxide field – the driving forces of NBTI degradation

Having exemplary investigated in the previous sections the basic characteristics of time and duty cycle dependence of degradation and recovery for a singe stress temperature (125 °C) and a single electric field (6.3), we are going to extend the study in the following to different stress conditions in order to draw fundamental conclusions on the temperature and field acceleration of NBTI. Following Eq. 3.1 and Eq. 3.2, the crucial parameters necessary to fully describe the degradation branch () are the pre-factor corresponding to the shift at = and the power-law exponent representing the slope of the degradation traces in a double-logarithmic plot vs. . On the other hand, the recovery branch may be fully described by the recovery rate alone, provided the relaxation traces follow a logarithmic time dependence ()).

In this section we study only the dynamics of degradation and recovery calculated from drain current variations recorded at a gate voltage close to the threshold voltage of the device. In particular, we abstain from analyzing the evolution of the CP current for different stress temperatures. Since the energy range, profiled during a CP measurement (), depends on the analyzing temperature (cf. Eq. 2.35), it could eventually lead to misleading conclusions, when comparing CP currents recorded at different temperatures. Consider that so far the simple MSM procedure is constrained to the limitation that the stress temperature () has to equal the recovery temperature (). A more elaborate procedure allowing to overcome this constraint is presented in Chapter 6 which also includes a detailed discussion of the temperature dynamics of the CP current.

All experiments discussed in this section are performed on different PMOS devices (SM6P/30/STD1). Due to the fact that the static OTF procedure is unfeasible on 30 HV devices and because of other drawbacks (discussed in Section 3.1), we record the degradation dynamics by making use of the MSM technique, thereby accepting some ‘undefined’ recovery when switching from the stress level () to the read-out bias (-1.1). The MSM procedure is performed by interrupting the DC stress phase once in a while for a short interval of time where the drain current is recorded with a stress-measurement delay is 10 at -1.1 which is close to the threshold voltage of the device. After a total stress time of 6,000 has elapsed, a continuous recovery trace is measured for 1,000 in order to collect information on the recovery dynamics as well.

3.4.1 The role of the stress/recovery temperature

The first set of measurements addresses the temperature activation of the shift and recovery. For that seven devices were stressed at the same oxide field of 5.5 applying different stress/recovery temperatures ranging from -60 °C to 200 °C, which corresponds to the full temperature range of our thermo chuck.

The data illustrating degradation and recovery are depicted in Fig. 3.10 (a), and (b), respectively. Fig. 3.10 (a) shows a power-law-like evolution of the degradation branch and Fig. 3.10 (b) a log-like evolution of the recovery traces. It is obvious that elevated temperatures cause larger degradation justifying the letter ‘T’ in NBTI.

For closer inspection, the data has been analyzed with respect to the temperature dependence of the coefficients describing the degradation ( and ) and the recovery branch (). The results are given in Fig. 3.11. Actually, the dependence of on T may be approximated either by an Arrhenius law with = as suggested by Schroder et al. [10] and by Kaczer et al. [27, 73, 74] or by a polynomial fit of second-order. Following Kaczer et al., an exponential relationship between the pre-factor and the stress temperature may be explained by considerations regarding disorder controlled hydrogen diffusion kinetics. On the other hand, following Bindu et al. [75], a polynomial T-dependence may be explained by inelastic oxide hole trapping, where the linear contribution is assumed to account for the temperature dependent enhancement of the surface hole concentration during stress and the quadratic contribution accounts for a multiphonon-emission process which is assumed to govern threshold voltage degradation predominantly at low stress times.

As opposed to the pre-factor , the power-law exponent is found to be temperature independent which is clearly visible in Fig. 3.11 (b). The error bars consider the standard deviation of from the proposed perfect power-law-like evolution of the degradation branch. The small deviations are likely due to parasitic recovery occurring within the short time delay between removal of stress and the actual measurement (10). It has to be emphasized that the observation of a temperature independent power-law exponent is in contradiction to some proposed NBTI models in literature, where it has been suggested that at least the dynamics of interface state creation are supposed to produce temperature dependent power-law exponents due to either dispersive hydrogen diffusion within the oxide [27, 73, 74] or (according to an alternative model) due to dispersive reaction kinetics [8] controlling hydrogen release from Si–H bonds at the interface. We remark that those conclusions were drawn either from MSM experiments suffering from a considerably larger stress-measure delay than ours’ [12, 73] or from CP current measurements [8] which profile different ranges within the silicon bandgap when performed at different temperatures, cf. Fig. 2.8. In agreement with our findings, Alam et al. have demonstrated in [76] that the temperature dependence of the power-law exponent disappears (at least for thin oxide technologies) when applying the ‘recovery free’ OTF technique.

Fig. 3.11 (c1) and (c2) show the recovery rates as a function of T in an Arrhenius plot, and in a linear plot, respectively. Within the time scale of our experiment follows apparently a dependence. Except for the data recorded at -60 °C, the recovery rates are found to be only weakly temperature dependent, yielding a universal recovery rate of approximately -3.0, similar to the one obtained for the high– device (HK2P/1.5/1) in Fig. 3.2. The evolution of the pre-factor as a function of temperature may be described best by a second-order polynomial fit (cf. Fig. 3.2 (c2)). The Arrhenius-like exponential approximation gives unsatisfactory results. Note that the universal recovery rate of -3.0 does not necessarily imply that recovery is generally temperature independent considering that the prior stress phase was performed at variable temperatures as well, leading to different points of origin of the individual recovery traces.

In order to study the phenomenon in a more sophisticated way, it would be highly expedient to have a technique available which allows to bring devices to the same degradation level (by stressing them under the same oxide field and temperature) but monitor their recovery at arbitrary relaxation temperatures. A tool being able to switch the device temperature with maximum precision within a minimum of time would have the power to overrule the so far strict constraint that the stress temperature has to equal the recovery temperature. Such a tool was found in the so-called ‘in-situ polyheater’ technique. The implementation, calibration and application of particularly designed polyheater was one of the main achievements of this PhD thesis, allowing to investigate the influence of temperature on NBTI degradation and recovery in an unprecedented manner. The technique is introduced and utilized in Chapter 6.

3.4.2 The role of the stress field

The second set of measurements addresses the field activation of degradation and its implication on recovery. Again, seven different PMOS devices (SM6P/30/STD1) were stressed, however, this time a unique temperature of 100 °C was applied, but varying the stress field from 4.5 to 7.2. The data illustrating degradation and recovery are depicted in Fig. 3.12 (a), and (b), respectively.

As already obtained previously for different stress temperatures, Fig. 3.12 (a) reflects a power-law-like evolution of the degradation branch for different stress fields as well and Fig. 3.12 (b) the like evolution of the recovery traces. An exception to the rule in found for the 7.2 data which begins to deviate considerably from the power-law-like characteristic after 1,000 of stress, indicating the onset of a different degradation mechanism. At elevated stress biases (fields) a larger amount of degradation is observed, justifying the letter ‘B’ in NBTI. An important difference to the temperature characteristics in Fig. 3.10 regards the shape of the recovery traces recorded at -1.1 after electrical stress at different fields. As opposed to the recovery characteristics obtained for different temperatures, the recovery traces recorded at different stress fields become considerably steeper with increasing stress field. For example, the ‘175 °C at 5.5’ data in Fig. 3.10 (b) and the ‘100 °C at 6.5’ data in Fig. 3.12 (b) display similar degradation levels () post stress, but recover with completely different relaxation rates (175 °C at 5.5: ;100 °C at 6.5: ). The different relaxation behavior indicates that elevated stress temperatures may generate defects providing much larger relaxation time constants than defects generated by elevated electric fields. Those defects created at high stress temperatures (175 °C) and moderate electric fields (5.5) obviously do not recover significantly within our experimental time scale, although the recovery temperature itself is as large as well. This is a fundamental finding raising the question whether possibly more than one single defect type is involved in NBTI.

For closer inspection, the data has been analyzed with respect to the field dependence of the coefficients describing the degradation ( and ) and the recovery branch (). Fig. 3.13 (a) reveals a considerable field dependence of the initial degradation rate (). The full symbols reflect the analysis of the 100 °C data whereas the open symbols show the 200 °C data (not given in Fig. 3.12).

Again, the development of with may be approximated either in an exponential manner (Arrhenius) with = as suggested by Schroder et al. [10] or by a polynomial fit of second-order as suggested by Grasser et al. and Bindu et al. [53, 75]. Note that the ‘electric field factor’ in Fig. 3.13 (a1) is identically for 100 °C and 200 °C. The polynomial field dependence in Fig. 3.13 (a2) may be explained when assuming inelastic hole trapping during the early stages of stress: The quadratic dependence is then reflected by the field dependence of the multiphonon-emission process while the linear contribution accounts for the linear field dependence of the surface hole concentration.

Similar to the observations at different stress temperatures, the power-law exponent is found to be widely field-independent which is clearly visible in Fig. 3.12 (b) (full symbols 100 °C; open symbols 200 °C) and consistent with the bulk of literature [77, 76, 8, 78]. The result is, however, in contradiction to the work of Reisinger et al. [15] who reported a decrease of for similar thick oxide devices (7 – 15) in the stress field range of 3.0 to 6.0.

Fig. 3.13 (c1) and (c2) show the recovery rates as a function of in an Arrhenius plot, and in a linear plot, respectively. As opposed to the variable temperature experiment, the recovery rates recorded after NBTS at different stress fields are found to be exponentially stress bias dependent giving a similar temperature independent ‘electric field factor’ of 0.54 as obtained during stress ( = ), cf. Fig. 3.12 (c1). The recovery rates may be approximated by a polynomial fit of second-order as well, cf. Fig. 3.12 (c2). The larger the stress bias, the steeper the recovery slope, indicating that a larger amount of defects having time constants within the time scale of our experiment are activated during stress, and anneal during recovery, respectively. The evolution of shows apparent similarities to the evolution of , suggesting a symmetry of stress and relaxation when investigating NBTI at different stress fields but at a single stress/relaxation temperature. This symmetry is violated when introducing a different stress temperature (i.e. 200 °C), cf. open symbols). While the recovery rate remains independent of temperature, the degradation rate shows an offset at elevated stress temperatures. This indicates that there might be a quasi-permanent contribution of degradation which becomes activated during stress but does not recover within the time scale of our experiment.

3.4.3 Recovery saturation

In the previous subsections the recovery branch was found to follow a dependence with being the recovery rate per decade. This behavior was, however, so far only demonstrated for the cases where the stress time considerably exceeds the recovery time (). To elaborate whether the recovery changes its characteristic time dependence for and whether a permanent offset remains after long relaxation times is subject of this subsection.

In order to address this question, we have stressed a PMOS device at 200 °C and 5.5 for a short time of only 1 and subsequently monitored its recovery for 50,000 at -1.1. The result of this experiment is illustrated in Fig. 3.14. Following Fig. 3.14, we clearly observe two different recovery rates, indicating the presence of at least two different kinds of defects with considerably different relaxation time constants. The first is dominant within a 10 lasting period after terminating stress () and has a similar magnitude as obtained in previous experiments (-1.8). Between 10 and 1,000 the recovery slope levels off considerably toward a value of only -0.08.

Complete stabilization of the threshold voltage shift could not be obtained even after 50,000 of recovery. A final, ‘quasi-permanent’ degradation plateau of approximately 1.0 remains. We call the remaining degradation plateau ‘quasi-permanent’ since it is not completely constant but shows considerable slower relaxation dynamics compared to the initial steep recovery branch.