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5 Impact of Mixed NBTI/HC Stress on MOSFET Characteristics

BTI and HCD are among the most important reliability issues in modern devices. However, as already discussed in the previous chapters, these degradation mechanisms are typically studied in idealized settings. In particular, for BTI studies no voltage is applied to the drain, leading to homogeneous conditions across the oxide and thus to a homogeneous degradation. As soon as \( | \)\( V_\mathrm {D} \)\( | \) is increased, degradation becomes more and more inhomogeneous and the contribution of HCD to the total degradation increases (see Subsection 2.3.1). Even though it is well understood that MOSFETs in real circuits are rarely subjected to idealized BTI or HCD conditions, there is only a limited number of studies available on the impact of the mixed stress conditions as illustrated schematically in Figure 3.1. Therefore, a thorough experimental study of the impact of mixed stress conditions on 2.2 nm \ch{SiON} pMOSFETs characteristics of a 130 nm commercial technology (\( V_{\mathrm {DD}} \) \( = \) −1.5 V and \( V_{\mathrm {th}} \) \( = \) 465 mV) is presented in this chapter, which contains the first experimental characterization at the single defect level.

As an introduction to this chapter, it should be again mentioned that the permanent component, on the one side, is attributed to the generation of interface and oxide defects, the hopping of \ch{H} through the oxide, and defects with large characteristic emission times. On the other side, the recoverable component of degradation is typically attributed to the emission events of previously charged oxide defects within experimentally feasible time slots (on the order of seconds or minutes). In the following, the focus lies mainly on the recoverable component of degradation.

5.1 Large-Area pMOSFET Characteristics

The characterization of recovery in large-area devices (\( W \) \( = \) 10 µm, \( L \) \( = \) 120 nm or 130 nm) has revealed that with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \) the recovery can be negligibly small. Figure 5.1 illustrates one measurement in this regard. In this measurement, seven cycles of 5 ks stress and 10 ks recovery at a constant \( V_{\mathrm {G}}^\mathrm {str} \) and each cycle increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \) were performed. \( \Delta V_{\mathrm {th}} \) was extracted from a single point measurement of \( I_\mathrm {D} \) at \( V_{\mathrm {G}}^\mathrm {rec} \) (constant voltage method introduced in Section 3.5). It can be seen that the threshold voltage shift during recovery (\( R \)), extracted according Equation 5.1 with \( t_\mathrm {rec,min} \) \( = \) 3 ms, reduces with \( V_{\mathrm {D}}^\mathrm {str} \). For example, the recovery trace after \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −2.8 V (red trace) recovers less than 1 mV in 10 ks.

Figure 5.1: Recovery after mixed NBTI/HC stress: Seven cycles of 5 ks stress and 10 ks recovery at a constant \( V_{\mathrm {G}}^\mathrm {str} \) and increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \) were performed. Top: Recovery traces show the reduction of \( R \) with \( V_{\mathrm {D}}^\mathrm {str} \). Bottom: Com- parison of \( R \) and a simulation using an electrostatic model. A discrepancy between \( R_\mathrm {measured} \) and \( R_\mathrm {model} \) can be seen, especially at \( V_{\mathrm {D}}^\mathrm {str} \) \( < \) −2 V. \( R \) can be negligibly small (less than 1 mV in 10 ks of recovery) after mixed NBTI/HC stress. Figure source: [105].

(5.1) \begin{equation} \label {Eq:Recovery} R=|\Delta V_\mathrm {th} (t_\mathrm {rec}=t_\mathrm {rec,min})-\Delta V_\mathrm {th} (t_\mathrm {rec}=t_\mathrm {rec,max})| \end{equation}

\( R \) \( \Delta V_\mathrm {th} \) shift during recovery (recoverable component)
\( \Delta V_\mathrm {th} \) threshold voltage shift
\( t_\mathrm {rec} \) recovery time
\( t_\mathrm {rec,min} \) lower limit of the experimental window during recovery
\( t_\mathrm {rec,max} \) upper limit of the experimental window during recovery

The measurement data are compared to a simulation using an electrostatic model as introduced in Subsection 2.3.1. This model takes into account a lateral position dependent threshold voltage shift based on a linear approximation of the channel potential under stress according to Equation 2.54. This approximation is valid for lateral positions at the inversion state. At the pinch-off, the channel potential can be calculated using Equation 2.55. In this regard, it is discussed in Subsection 2.3.1 that using an electrostatic model, it is expected that recovery is reduced after stress with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \) because drain-side defects most probably will not contribute to recovery due to the reduced \( E_\mathrm {OX} \). However, source-side defects should be nearly unaffected by \( V_{\mathrm {D}}^\mathrm {str} \) and contribute to \( R \) independently from the drain bias.

Although an electrostatic model describes the behavior of \( R \) after NBTI rather well, Figure 5.1 bottom shows discrepancies between the experimental data and the simulation after mixed NBTI/HC stress. The measurements summarized in this figure, as well as measurements in [26], indicate that \( R \) can be negligibly small after mixed NBTI/HC stress. This would mean that almost no oxide defects contribute to the recoverable component. This contradicts the assumption that source-side defects contribute nearly unaffected to \( R \). Since oxide defects are uniformly distributed all over the device area, such a behavior cannot be explained by an inhomogeneous \( E_\mathrm {OX} \) only.

In order to analyze the origin of the discrepancies between the experimental data and the simulation, interplay between NBTI and HCD in large-area devices is studied. For this, the eMSM measurement method was used according to Section 3.5 and extracted \( \Delta V_{\mathrm {th}} \) from a single point measurement of \( I_\mathrm {D} \) at \( V_{\mathrm {G}}^\mathrm {rec} \) during recovery (constant voltage method). 58 devices were measured at \( T \) \( = \) 130 °C using the following phases:

From these measurements following was extracted:

Figure 5.2: Degradation after stress: \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) was extracted at \( t_\mathrm {rec,min} \) \( = \) 3 ms. Top: For \( t_\mathrm {str} \) \( = \) 20 ms the reduction of \( E_\mathrm {OX} \) across the gate oxide near the drain re- gion suppresses NBTI with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \). For larger \( t_\mathrm {str} \) it can be seen that with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \), the interplay between NBTI and HCD leads to two local minima of \( \Delta V_{\mathrm {th}}^\mathrm {AS} \), at \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −0.5 V and \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −2 V. Center: Similar to the top panel. With increasing stress time a drift minimum starts to form at \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −0.5 V. Bottom: The minimum of \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) at \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −0.5 V forms clearly for \( t_\mathrm {str} \) \( = \) 11.1 s and \( t_\mathrm {str} \) \( = \) 1.11 ks as discussed in [25, 26]. Figure source: [124].

From Figure 5.2 it can be seen that local degradation minima form after stress depending on the stress voltages and on the stress time. While after \( t_\mathrm {str} \) \( = \) 20 ms \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) decreases or stays constant with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \), for longer stress times \( t_\mathrm {str} \) \( > \) 10 s a drift minimum forms around \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −0.5 V. Quite interestingly, for \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V a second minimum forms at \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) −2 V. The dependence of the formation of such minima on \( t_\mathrm {str} \) is confirmed by the data of Figure 5.3 for the two cases \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V and \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −2.5 V. Especially for \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V it can be seen that if \( t_\mathrm {str} \) \( < \) 100 s and \( V_{\mathrm {D}}^\mathrm {str} \) \( < \) 0 V, \( \Delta V_{\mathrm {th}} \)\( ( \)\( t_\mathrm {str} \)\( ) \) is always lower than for homogeneous NBTI.

(a) Low gate bias: \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V.

(b) High gate bias: \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −2.5 V.

Figure 5.3: Stress and recovery traces at two different gate stress biases: The \( \Delta V_{\mathrm {th}} \) drift during stress depends strongly on \( t_\mathrm {str} \). Below 100 s the degradation at \( V_{\mathrm {D}}^\mathrm {str} \) \( = \) 0 V (NBTI) dominates. Above this stress time degradation is more and more dominated by the HC regime. Figure source: [124].

It has already been discussed in literature [25, 26] that drift minima such as shown in Figure 5.2 occur for long stress times. This behavior was explained by competing processes contributing to the degradation: while sweeping \( V_{\mathrm {D}}^\mathrm {str} \) from 0 V to, e.g., −3 V, \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) reduces first due to the fact that \( | \)\( E_\mathrm {OX} \)\( | \) decreases at the drain-side and, as a consequence fewer drain-side defects capture charge carriers. From a certain \( V_{\mathrm {D}}^\mathrm {str} \) on, this effect is compensated by the contribution of HCD to \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) which leads to an increase. However, this behavior has not been observed for all \( V_{\mathrm {G}}^\mathrm {str} \) and \( t_\mathrm {str} \) in the measurement. For example, \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) reduces at \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V and \( t_\mathrm {str} \) \( = \) 20 ms with increasing \( | \)\( V_{\mathrm {D}}^\mathrm {str} \)\( | \) without forming any drift minima. It can be concluded that whether and where a minimum forms in \( \Delta V_{\mathrm {th}}^\mathrm {AS} \) depends strongly on the stress time and on the gate and drain bias.

(a) Degradation of the linear drain current: \( I_\mathrm {D,lin} \) extracted at \( V_\mathrm {D} \) \( = \) −0.1 V and \( V_\mathrm {G} \) \( = \) \( V_{\mathrm {DD}} \).

(b) Degradation of the saturation drain current: \( I_\mathrm {D,sat} \) extracted at \( V_\mathrm {D} \) \( = \) \( V_\mathrm {G} \) \( = \) \( V_{\mathrm {DD}} \).

Figure 5.4: Degradation of the drain current in the linear and saturation regime: While the degradation behavior at \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V and \( t_\mathrm {str} \) \( = \) 1.11 ks is comparable to the results in literature, the curves for \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V and \( t_\mathrm {str} \) \( = \) 11.1 s show that \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) is higher for lower stress times at certain \( ( \)\( V_{\mathrm {G}}^\mathrm {str} \)\( , \)\( V_{\mathrm {D}}^\mathrm {str} \)\( ) \) combinations. This means that the degradation evo- lution of both turns around during stress. Similar behavior was also observed for the degradaton of \( g_\mathrm {m,max} \) and \( SS \). Figure source: [124].

The analysis of the degradation of \( I_\mathrm {D,lin} \) and \( I_\mathrm {D,sat} \) illustrated in Figure 5.4 shows a strong dependence on \( t_\mathrm {str} \) as well. After \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V and \( t_\mathrm {str} \) \( = \) 1.11 ks, a minimum in the \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) curves can be seen around \( V_{\mathrm {D}}^\mathrm {str} \) \( \approx \) −1 V, which is comparable to the results in literature [25]. Remarkably, the measurements show that after shorter stress with \( t_\mathrm {str} \) \( = \) 11.1 s \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) are higher at a certain \( V_{\mathrm {D}}^\mathrm {str} \) than after stress with \( t_\mathrm {str} \) \( = \) 1.11 ks also at \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −1.5 V. This means that with increasing stress time both first increase, then this trend obviously turns around and they decrease again. Such a behavior has not been observed for higher gate bias \( V_{\mathrm {G}}^\mathrm {str} \) \( = \) −2.5 V in these measurements. For a detailed analysis of the time dependent \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) evolution at higher gate stress bias, ten devices were measured using the MSM method (see Section 3.4) with the following phases:

Figure 5.5: Degradation and recovery of the drain current in the linear and in the saturation region as well as the threshold voltage shift: The degradation and recovery were measured by short interrupts of the stress and recovery phase in order to measure \( I_\mathrm {D,lin} \) and \( I_\mathrm {D,sat} \). Especially \( \Delta I_\mathrm {D,lin} \) but also \( \Delta I_\mathrm {D,sat} \) show a local maximum after one second of stress, a local minimum after approximately ten seconds of stress, and increases for larger stress times. No turn-around effect was measured for \( \Delta V_\mathrm {th} \).

From the \( I_\mathrm {D} \)-\( V_\mathrm {G} \) characteristics \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) are extracted during stress and recovery, which can be seen in Figure 5.5. It has to be noted that a small discrepancy occurs due to the interruptions of the stress and recovery phase compared to measurements without interruptions (also mentioned in Section 3.4). This is because each interruption during stress leads to a partial recovery of the degradation and each interruption during recovery slightly stresses the device. Therefore, the results from these measurements are shown as a schematic illustration but are not suitable as a basis for a further model development. The analysis of the degradation and recovery of \( \Delta I_\mathrm {D,lin} \) and \( \Delta I_\mathrm {D,sat} \) shows that local minima and maxima occur at higher gate bias as well. Depending on the stress voltage combination, \( \Delta I_\mathrm {D,lin} \) has a local maximum after one second of stress, followed by a local minimum after approximately ten seconds of stress.

Such stress-time dependent turn-arounds of degradation have already been observed recently [99, 100, 102] and discussed in Subsection 2.2.6. Although the explanation in the mentioned subsection cannot be applied to the measured \( \Delta I_\mathrm {D,lin} \) turn-around in the same way due to the different measurement methods, it gives an idea that II and the interplay of different types of defects together with the creation of secondary generated carriers triggered by II may determine the behavior of device degradation. However, these results merely suggest an interplay between NBTI and HCD and no detailed information about the particular processes at the single defect level can be extracted from these measurements. Thus, the impact of mixed NBTI/HC stress on the behavior of single defects was analyzed and the results are presented in the next subsection.

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