3 Dynamics of NBTI degradation and recovery

When subjecting a PMOS device to NBTS, the amount of degradation is reported to increase gradually as a function of stress time, electric field and temperature, leading to a characteristic reduction of the MOSFET performance. However, once the stress bias is removed, at least a certain fraction of the total shift is reported to recover very quickly, making the delay between the point of time of stress termination and the first measured point recorded at the threshold voltage of the device () an important parameter, which crucially determines the amount of degradation detected at the end of stress (). The degradation and the recovery of the threshold voltage shift may be approximated empirically by power-laws:

where the pre-factors and are reported to depend on the oxide field during stress () and recovery () as well as on the stress temperature () and the recovery temperature (). The power-law exponents and determine the degradation and recovery dynamics as a function of the stress () and the recovery time (). and are extracted from the slope of the shift in a double-logarithmic plot vs. , and vs. respectively. Note that the second term in Eq. 3.1 accounts for power-law-like recovery after interrupting the stress phase. It may be neglected when the stress time () exceeds the measurement delay () by far (provided the overall dynamics of degradation and recovery are similar).

Long-term degradation ( ) is reported to follow a typical power-law-like increase with . On the other hand, short-term degradation ( ) and recovery show much smaller power-law exponents ( and ), allowing to approximate Eq. 3.1 by logarithmic time dependences. This can be easily demonstrated by expanding the power-law relations in Eq. 3.1 in Taylor series around small values of , and , respectively, yielding

where is the degradation rate and is the recovery rate in mV/decade. Assuming NBTI to be caused by hole trapping within the gate oxide (as it is possibly the case for short stress times), and can be approximated by the minimum capture time constant and the minimum emission time constant at the particular stress/relax conditions after Huard et al. [51]. Universality of recovery traces ( vs. ) recorded at different stress times has been demonstrated by Grasser et al. in [52] and may be obtained when assuming and and , yielding the following simplified expression for the threshold voltage shift:

When neglecting recovery (), we may derive the degradation dynamics from Eq. 3.2 as follows:

In [53] universal scalability of the short-term and long-term degradation and the recovery has been demonstrated for different stress fields, temperatures and oxide thicknesses suggesting either a single mechanism or at least tightly coupled phenomena to be responsible for NBTI induced degradation and recovery.

The dynamics of both branches, namely the evolution of the degradation as a function of the stress time, field and temperature and the evolution of the recovery as a function of the recovery time, field and temperature, are very important indicators used to evaluate the NBTI stability of a technology and to check theoretical predictions derived from particular physical models. Since degradation usually follows a power-law with (except for short stress times) which cannot be perceived as log-like, it is typically described by the pre-factor and/or the power-law exponent . On the other hand, (at least when being far away from recovery saturation) relaxation usually follows a power-law with which is similar to log-like. Hence, the recovery rate per decade (pre-factor ) in mV/dec (when measuring ) recovery or in A/dec (when measuring CP current recovery) can be used to fully describe relaxation dynamics.

In this chapter, different techniques are presented which allow to investigate the dynamics of defect generation and recovery under AC and DC bias conditions as a function of stress time, recovery time, temperature and electric field. By means of case studies performed optionally on thin high– and/or thick SiO devices, fundamental experimental signatures of NBTI are revealed helping to catch a glimpse of the multi-faceted features and complexity of the problem.

3.1 Static MSM and OTF

So far, the two most frequently used measurement techniques for evaluating NBTI dynamics during stress and recovery are the classical measure/stress/measure (MSM) technique and the OTF measurement method [54]. Both techniques have certain advantages and drawbacks making the method of choice dependent on the particular problem [55, 56]. The biasing conditions applied during static MSM and OTF are schematically depicted in Fig. 3.1.

When applying the MSM technique, a single device is usually stressed repeatedly with increasing stress () and recovery times () following a geometric progression. Thereby it is usually assumed that the amount of defect relaxation occurring during the last recovery period is fully restored at the end of the subsequent longer-lasting stress run. After each stress run, the gate bias is switched from the stress level () to the threshold voltage of the device. In parallel the drain bias is switched from 0.0 to the particular read-out bias () initializing the drain current measurement as a function of the recovery time , and the stress time , respectively. In the data analysis, the drain current degradation (recorded at the threshold voltage) is converted into a corresponding shift () by assigning the degraded current values a corresponding gate voltage recorded at the virgin device, cf. Chapter 2.

Hence, the MSM technique provides the feature to analyze shifts as a function of the stress and the recovery time, the gate bias being typically (but not necessarily) close to the threshold voltage of the device during read-out. One important drawback of the technique is the fact that the extracted shifts are always afflicted with an unknown amount of recovery occurring between the point of time after removal of the stress bias and the first measurement of the drain current at the threshold voltage of the device, cf. Eq. 3.1. For experimental reasons, the switching event and the following measurement cannot be performed arbitrarily fast (), leaving much room for speculation what happens within the first couple of nanoseconds after terminating stress. Until now, only a few groups claim that they seriously succeed in finding a plateau in their recovery curves at very early recovery times. By using the Ultra-Fast VT (UFV) measurement method [57], a minimum delay time in the range of microseconds was achieved [58, 59]. Although quite promising, a possible explanation for this observed plateau has been given in [60] as being due to the difficulty of synchronizing the recovery time scale with the real end of stress. In most reported cases, however, the extracted recovery curves are straight lines in a logarithmic time plot, indicating a very low starting time of the recovery event which remains apparently inaccessible even when advancing toward the microsecond regime [61].

When applying the OTF technique, the drain current degradation is monitored directly under stress bias conditions, making the measurement procedure itself quasi recovery-free. At the moment the gate bias is switched from the threshold voltage to the stress level (), the drain current measurement is started instantaneously, with the read-out drain bias applied also during stress. In order to convert the degraded drain currents recorded under stress bias conditions () into corresponding shifts (), the first current value recorded at is usually considered as virgin (), yielding the following expression for the threshold voltage shift measured during OTF (cf. Eq. 2.5):

As opposed to the shift measured at the actual threshold voltage of the device, contains a parasitic component caused by mobility degradation (cf. 2.1.2) making it difficult to compare and directly. In order to estimate the parasitic mobility impact of , the classical OTF technique has been extended to a so-called second level or three level OTF procedure were the gate voltage is varied slightly around the stress bias every time a drain current measurement is required allowing to estimate the variation of the transconductance around the stress voltage [54]. Besides the mobility influence, the OTF technique suffers from an additional handicap concerning the definition of the first measured drain current value : Eq. 3.6 assumes to be the virgin drain current at the stress voltage, however, when considering degradation and recovery as similarly fast, is actually already degraded to a certain degree, again leaving much room for speculation about what happens in the first picoseconds after initiating stress [62]. From an application point of view, the OTF technique is only feasible when studying thin oxide technologies having their stress biases () not far away from their threshold voltages (). This is because the signal vs. noise resolution of the relative drain current degradation decreases linearly when increasing the gate voltage overdrive, cf. Eq. 2.5.

In order to demonstrate the dynamics of NBTI stress and recovery, a 1.5 high– PMOS device equipped with a p gate poly (HK2P/1.5/1) was stressed for 100 at 125 °C using a stress voltage of -2.0, cf. Fig. 3.2. Following Eq. 1.7, -2.0 corresponds to an oxide field of approximately 6.6. During the stress period, the linear drain current ( = -) was monitored and was calculated using Eq. 3.6. was measured 10 after applying the stress bias. Subsequently to the stress phase, the gate bias was switched to the threshold voltage of the device (-0.3) recording the linear drain current then under recovery bias conditions. During recovery, was calculated by referencing the degraded drain current to a gate voltage corresponding to the virgin transfer curve. As can be seen in Fig. 3.2 (a), during stress the threshold voltage shift () increases rapidly achieving 44 after 100 stress. At that moment, the stress bias is switched from -2.0 to -0.3, the obtained threshold voltage shift measured under recovery conditions () is considerably reduced by 24 within the first 10 after removal of the stress bias. The large gap between the last measured point of and the first measured point of indicates fast recovery, although probably not the entire 24 gap may be attributed to trap annealing since is likely to contain an offset caused by mobility degradation.

Fig. 3.2 (b) illustrates that both and increase and decrease more or less linearly in a double logarithmic diagram indicating a power-law-like correlation between degradation and stress time () as well as between relaxation and recovery time () as suggested in Eq. 3.1. Note that due to the small power-law factor associated with recovery, we may describe the relaxation branch also as being log-like with a recovery rate of = -. The power-law factor measured during OTF stress () is found to be 0.18 which is pretty close to the factor 1/6 often reported in literature. The kink in the stress curve visible at early stress times may be a consequence of the fact that , measured 10 after applying the stress bias, is actually already degraded to a certain degree, distorting the shift evaluation in particular at the beginning of the stress phase where the overall degradation is low.