Monitoring ID at VTH

2.1.1 Monitoring $ID$ at $VTH$

One way to assess the NBTI degradation has been suggested by Kaczer et al. [17, 18], who switch $VG$ close to the threshold voltage $VTH$ after stress and at the same time monitor the degraded and now recovering drain current $ID$ over time. By approximating the initial and the degraded $ID(VG)$ -curve with quadratic polynomials and assuming that the degradation does not change the form of the initial polynomial approximation, one obtains

AV 2TH,0 + BVTH,0 + C1 = ID,0, (2.1) 2 A(VTH,0 + ΔVTH ) + B (VTH,0 + ΔVTH )+ C2 = ID,0. (2.2)

Equating these two yields

2 AΔV TH + (2AVTH,0 + B )ΔVTH + C◟2◝−◜-C1◞ = 0, −ΔID

(2.3)

and solving the quadratic form of $ΔVTH$ leads to

∘ -------------2---------- ΔVTH,12 = −-(2AVTH,0-+-B-)±---(2AVTH,0-+-B-)-+-4A-ΔID-. 2A

(2.4)

Using (2.1) and adding $ID$ on both sides yields

− AV T2H,0 − BVTH,0 − C1 + ID = − ID,0 + ID . ◟---◝◜---◞ ΔID

(2.5)

Inserting (2.5) into (2.4) finally gives a formula which only depends on $VTH,0$ and $ID$ . The $ΔVTH$ -shift to the right, respectively the decreasing $ΔID$ is displayed in Fig. 2.1.

∘ --2--------------- ΔVTH = − (2AVTH,0-+-B-)±--B--−-4AC1--+-4AID-- 2A

(2.6)

Figure 2.1: Schematic picture of an $ID(VG )$ -curve before and after stress. The resulting degradation is usually given in terms of $ΔVTH$ or $ΔID$ .

This measurement method is generally performed using standard off-the-shelf instruments. Due to the fact that this equipment is not targeted for time-critical measurements, the shortest achievable measurement delays $tM$ only reach down to about $1ms$ .

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2.1.1 Monitoring at

2.1.1 Monitoring $ID$ at $VTH$