Yannick Wimmer Dipl.-Ing. Publications

Hole trapping in the gate insulator of pMOS transistors has been linked to a wide range of detrimental phenomena, including random telegraph noise, 1/f noise, Negative Bias Temperature Instability (NBTI), stress-induced leakage currents and hot-carrier degradation. In Time-Dependent Defect Spectroscopy (TDDS) measurements, it was observed that the defects tend to dis- and reappear in the measurements (see Fig. 1). This so called volatility is not a rare event, but can under certain circumstances occur for a majority of the defects. Recently we were able to show that the hydroxyl E’ center (H-E’) (see Fig. 2) is a likely candidate for these defects in amorphous silicon dioxide (a-SiO₂). We speculate that the behavior could be explained by the hydrogen atom moving away from the defect site onto a neighboring oxygen atom and back again. Our model for NBTI consists of four states (1,1',2',2) that are necessary to explain the complex NBTI behavior (see Fig. 2).
For explaining the volatility we investigated the energy barriers E_B of a hydrogen atom moving from the positively charged defect site to a particular neighboring oxygen atom, resulting in the new configurations 0⁺ and 0ⁿ. The resulting configurations of state 0 can be divided into three categories based on their behavior in state 0ⁿ (see Fig. 3): The hydrogen atom can either stay bonded to the neighboring oxygen, become interstitial, or break up one of the Si-O bonds at its new position, resembling state 1 of the H-E’. Fig. 2 provides a cut through the potential energy surface along the reaction coordinates for the different state changes. Note that in this six-state model there are now three possibilities to leave state 2' (to 1, 2 or 0⁺). Note also that if the barrier 0⁺→ 0ⁿ were to be overcome, the hydrogen would become interstitial in 0ⁿ. If it then diffuses away, this mechanism would provide a possible explanation for a defect disappearing entirely. However (especially in the case where the hydrogen does not become interstitial in 0ⁿ) the defect would only be electrically inactive if the barrier 0⁺→ 0ⁿ is high enough. Since all calculations have to be carried out in a-SiO₂, results differ for each of the used structures, resulting in distributions.
The calculated distributions contain barriers E_B low enough and E_f high enough (see Fig. 2) to provide a possible explanation for the various forms of volatility observed, emphasizing that the H-E' is a possible candidate for the dominant NBTI defect.

Fig. 1: Measured defect activity of defect I2 extracted from TDDS measurements during the first 200k seconds of the measurement.

Fig. 2: Example of a cut through the potential energy surface of a H-E’ defect along the reaction coordinates between different states. Possible changes of states can occur by nonradiative multi-phonon transitions (green arrows) or barrier hopping (purple arrows). The BTI-active states are depicted on the left side of the plot (orange). When it overcomes the barrier 2 → 0⁺ it is BTI-inactive (grey area) and therefore not visible in the measurements, given that the barrier between the states 0⁺ and 0ⁿ is too high to be overcome under measurement conditions.

Fig. 3: Examples of different states 0 with different behavior in the neutral state 0ⁿ: Top: The hydrogen atom (white) moves to a neighboring oxygen atom (red) where it stays attached, also in the state 0ⁿ. Middle: At the oxygen atom where the hydrogen atom moves to, one of the oxygen-silicon bonds breaks in 0ⁿ. Bottom: The hydrogen atom only sticks to the neighboring oxygen atom in the state 0⁺, but becomes interstitial when charged neutrally (0ⁿ).