Temperature and Voltage Dependence of Universal Law

4.2.1 Temperature and Voltage Dependence of Universal Law

Up to now it was only shown that the universality holds for various pMOS/nMOS-NBTI/PBTI-combinations. As temperature and voltage acceleration play an important role for lifetime projection, the study of the universal relaxation is now extended towards these stress conditions. How the two components $R$ and $P$ behave is therefore analyzed under different stress temperatures $T$ and stress voltages $VS$ , cf. Fig. 4.7. In this graph only the last long relaxation tail of the MSM-sequence is depicted. The different stress conditions described by the relaxation model (4.5) yield excellent agreement with the measurement results. The activation energies $E A$ are extracted for $B$ and $β$ , and the components of $R$ and $P$ . They are depicted in Fig. 4.8. While $R$ and $B$ show an Arrhenius-like behavior with $EA ≈ 0.08eV$ respectively $0.04eV$ for different stress times, $β$ is constant. $P$ on the other hand depends on the stress time, which rules out Arrhenius-like behavior [6, 30].

Figure 4.7: When only the last relaxation sequence after $20000s$ stress is considered under various temperatures (Top) and voltages (Bottom), the fit shows universal behavior.

Figure 4.8: Using different stress times and temperatures allows to extract activation energies in an Arrhenius plot for the four components $R$ , $P$ , $B$ , and $β$ in our relaxation model (4.5). While $R$ and $B$ are Arrhenius, $P$ is not (due to different values of $EA$ ), and $β$ is constant.

[next] [front] [up]