On-The-Fly (OTF)

2.3 On-The-Fly (OTF)

While the MSM-technique was conceived to capture the recovery following stress as fast as possible, a completely different approach was first proposed by Denais et al. [28]. In contrast to the discussion of the impact of fast recovery which cannot be determined prior to the measurement delay³ , the “on-the-fly” method measures the drain current at stress level without ever interrupting the stress. Due to the experimental setup of never allowing the device to reach the subthreshold regime during stress, the degradation during stress can only be monitored via the degradation of the linear drain current $ID,lin$ [31, 28, 14, 32, 33, 34, 12, 6]. Therefore, a method has to be found to convert this measured quantity into a parameter relevant at use-condition, e.g. $V TH$ .

Figure 2.7: Transfer characteristics plotted on a logarithmic- (left ordinate) and linear-scale (right ordinate). After stress the $ID (VG )$ -characteristics is shifted to the right. The change in the subthreshold-slope due to the increased interface state density affects the physically defined threshold voltage shift, which depends on the gate voltage, i.e. $ΔVTH (VG )$ . On the other hand $ΔV θ$ is an empirical quantity, as defined in (2.7). Note that $V θ$ is larger than $VTH (VG)$ in the subthreshold regime.

As mentioned in [12], the main problem of the OTF method is that the $VTH$ -shift has almost the same effect on the transfer characteristic as the degradation of the mobility. A shift of $VTH$ as a consequence of electrically active defect charges results in a pure vertical shift along the $VG$ -axis. More precisely this is because defect charges have a direct impact on the surface potential and hence on the threshold voltage (cf. equation (1.1)). On the other hand, defects located at the interface cause surface scattering. The thereby increased channel resistance (lower mobility) yields a lower drain current after stress and tilts the transfer characteristics. The resulting decrease in $ID$ than leads to a spurious increase of $VTH$ , in addition to the already mentioned $VTH$ -shift due to the total defect charge itself. Unfortunately, these two effects cannot be separated easily in the linear regime, as can be seen in Fig. 2.7. Due to the saturation of the drain current $I D$ a relative change in $I D$ becomes more and more insensitive to changes in $VTH$ with increasing $VG$ .

The degradation of $ΔVTH$ as defined in (1.1) is just attributed to the defect charges and is independent of the mobility. In contrast to that, $ID,lin$ recorded via the OTF technique does depend on $μeff$ [34, 35, 36], just as it reflects the existence of additional charges ( $ΔQot$ and $ΔQit$ ). To extract $ID,lin$ the simple SPICE compact model [37] valid in the linear regime under strong inversion only is used:

βVD-(VG-−-Vθ −-VD∕2)- ID,lin = 1+ θ(VG − V θ − VD ∕2) for VG > V θ.

(2.7)

While $β$ depends on $μeff$ , $θ$ models the mobility saturation with increasing vertical field and $Vθ$ , the threshold voltage, is obtained by the intersection of $ID,lin$ extrapolated to $ID,lin = 0$ , which is depicted in Fig. 2.7. Due to the fact that the interface charge depends on the gate voltage through the occupancy at the interface, as stated in (1.1), the threshold voltage is not a well defined quantity, i.e. $ΔVTH = ΔVTH (VG )$ [37, 38]. Equation (1.1) uses a physical definition of a threshold voltage, while $Vθ$ is a purely empirical quantity that yields the best fit to the level 1 model⁴ . It can be shown that it is important to provide a large $VG$ -range to get a reliable extraction of $Vθ$ .

The main issue with OTF is that as a matter of principle it is not possible to determine the initial $ID,lin$ at $tstr = 0$ , because due to the nonzero measurement time the device is already stressed, and so the first measurement yields $ID,lin(tstr > 0)$ . This pre-stressed value is then taken as a reference, which has a considerable impact on the subsequent extraction of the degradation [39, 40, 41].

Figure 2.8: Transfer characteristics plotted on a logarithmic- (left ordinate) and linear-scale (right ordinate). In contrast to the $ΔVTH$ -extraction in the subthreshold-regime, $ΔV θ$ has to be determined under strong inversion. Lowering the extrapolation range of $VG$ decreases the possibility of already pre-stressing the device, but causes an inaccuracy in the thereby determined $ΔV θ$ .

When the $VG$ -range is reduced as depicted in Fig. 2.8, at least for the pre-stressed transfer-characteristic, a value close to the initial value, i.e. $ID,lin(tstr ≈ 0)$ is obtained. On the other hand this method induces a large error, which is of the same order of magnitude as $ΔV θ$ itself. Therefore, it is not feasible to describe the $I D,lin$ -regime properly by reducing the $VG$ -range.

Different OTF models are based on (2.7) and are discussed in Appendix A in detail. Here the so-called OTF3 after Zhang et al. [34], displayed in Fig. 2.9, will be described. A change in $ID,lin$ can only be converted to $ΔV θ$ if the transconductance $gm$ , which is defined as the change of the $ID$ over $VG$ , is known. To get $gm$ , $ID$ is recorded while slightly varying $VG$ . This three-point measurement method [28] is indicated in Fig. 2.9 as well and yields

ID,lin(VG-+-ΔV--)−-ID,lin(VG--−-ΔV-) gm(n) = 2 ΔV .

(2.8)

By averaging $gm$ , $ΔV θ$ is finally obtained via the sum

N OTF,3 ∑ -ID,lin(n)−--ID,lin(n-−-1) ΔV θ ≈ − 1∕2 (gm (n)+ gm (n − 1)). n=1

(2.9)

In order to prevent a degraded reference of $ID,lin$ and $gm$ , Zhang et al. suggested to perform the oscillation of $VG$ with a rise and fall time of $6 μs$ . Considering such a “degradation-free” reference thus produces a higher amount of visible $ΔV OTF,3 θ$ -degradation [42] due to the down-shifted initial value of $ID,lin$ and $gm$ . Moreover, as $ΔVTH$ increases with $VG$ , the OTF-method measures a higher degradation ( $ΔV (I ) θ D,lin$ ) compared to the typical use-condition of a device ( $|VG,use| < |VG,str|$ ). OTF hence overestimates the “real” degradation. In contrast the “real” degradation is underestimated, when the evaluation of $VTH$ is based on DC transfer characteristics. As a consequence, the determination of the lifetime is heavily influenced by either measurement routine. Datasheet conditions on the other hand should better reflect the real degradation under real use-conditions of devices.

Compared to MSM, the biggest advantage of OTF is its recovery-free measurement routine while it is difficult to measure recovery with it, because the OTF technique originally was conceived only to record data in the stress phase of NBTI.

Figure 2.9: Schematic of the OTF3 methodology. Left: The three points symbolize the quantities at $VG$ and their small perturbation $± ΔV$ . The drain voltage $VD$ stays constant during the pulse. Right: The resulting $ID,lin$ whose two points $ID(n − 1)$ and $ID(n)$ are needed to determine the degradation of $ID$ . The shift of $gm$ is calculated via (2.8) by using the modulated $I (V ) D,lin G$ .

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