Anomalous random telegraph noise in nanoscale transistors as direct evidence of two metastable states of oxide traps

In this paper, a new pattern of anomalous random telegraph noise (RTN), named “reversal RTN” (rRTN) induced by single oxide trap, is observed in the drain current of nanoscale metal-oxide-semiconductor field-effect transistors (MOSFETs) with high-k gate dielectrics. Under each gate voltage, the rRTN data exhibit two zones with identical amplitudes but reversal time constants. This abnormal switching behavior can be explained by the theory of complete 4-state trap model (with two stable states and two metastable states), rather than the simple 2-state or improved 3-state trap model. The results provide a direct experimental evidence of the existence of two metastable states in a single oxide trap, contributing to the comprehensive understanding of trap-related reliability and variability issues in nanoscale transistors.


Experimental Results
Devices characterized in this work are planar high-k/metal-gate n-type MOSFETs with length L = 60 nm, width W = 300 nm and ultra-thin HfO 2 gate dielectrics. The experimental results of the anomalous RTN in drain current under different gate voltages V G are shown in Fig. 2, with the drain voltage kept at V D = 50 mV, and temperature T = 25 °C. For other V G , the anomalous RTN data are shown in Fig. S1 of the supplementary materials. It can be clearly observed that this RTN exhibits two zones (zone A & zone B) under the same bias. The results are repeatable after measurement interruptions. As illustrated in Fig. 3, the expanded detail shows that the capture time constant is smaller than the emission time constant in zone A, while it has the reversal feature in zone B. Therefore, it is named "reversal RTN" (rRTN) here.
To have quantitative information, the characteristics of the rRTN in zone A and zone B are carefully investigated in the following three aspects: amplitudes, time constants and trap position. The extracted amplitudes of RTN in zone A and B are shown in Fig. 4 only two current levels throughout the entire time domain. In principle, the RTN induced by N traps in a single device should be corresponding to 2 N current levels. Therefore, it is most likely that zone A and zone B represent the same trap, otherwise, there should be more than two current levels due to the superposition of RTN levels induced by more than one traps. The time constants τ c and τ e in each zone are extracted as shown in Fig. 4(b), and the extraction details are shown in Fig. S2 of the supplementary materials. Both τ c and τ e in two zones have the similar V G dependence, respectively. Therefore, based on the relationship 16,17   where T IL is the thickness of the SiO 2 interfacial layer and T HK the thickness of the HfO 2 high-k layer, ε SiO2 and ε HK are the dielectric constants for SiO 2 and the HfO 2 high-k dielectric, respectively, k B is the Boltzmann constant and T is the temperature, the vertical distance x to the oxide/channel interface can be attained. It is worth mentioning that since the RTN measurement region is above the threshold voltage in this work, the effect of ∂ψ S /∂V GS is small and thus is ignored for simplicity 18 . As shown in Fig. 4(c), the x/T OX extracted from two zones are 0.74 and 0.72, respectively, which are almost the same, suggesting the same trap location in the HfO 2 dielectric, thus providing another proof that two zones correspond to one single trap.

Discussions on Physical Mechanism
It is believed that, during the transition from one valence state to another, the trap may go through a metastable state 1,7,14 . In order to explain the mechanism of rRTN with two zones, all the possible trap models, i.e., 2-state, 3-state (with one metastable state) and 4-state (with two metastable states) trap models, are studied. First, the simple 2-state trap model originating from the normal RTN theory can be excluded apparently, because metastable states should be introduced to interpret the abnormal switching phenomenon. Next, the 3-state trap model with one additional metastable state is considered. It is worth noting that the 3-state trap model as shown in Fig. 1 cannot explain the rRTN, due to the fact that the switching phenomenon in rRTN is frequent throughout the  entire time domain with no "quiet" phase. Therefore, the 3-state trap model needs to be modified. There are two types of 3-state trap model can be the candidate transition modes, as shown in the inserted of Fig. 5(a,b). Based on the extracted time constants from these two zones, the transition probabilities between each two states can be calculated as follows: For the type I: 12 12 12 12 12 12 For the type II: The extracted transition probabilities under different V G are shown in Fig. 5(a,b). For the type I model, it can be found that P(1 → 2′) is about 1, and P(1 → 2) is close to 0. It can be deduced that if the transition from state 2 to 1 is very fast, the probabilities will lead to almost the same results as normal RTN with two current levels. If the transition from 2 to 1 is slow, there will be a long time period when the current is staying at the low level. Based on the extracted time constants, the RTN simulation with multiple states can be performed. The details of the theoretical simulation method are shown in Figs S3 and S4 in the supplementary materials, which is similar to ref. 19. The result is shown in Fig. 5(c). As expected, the 3-states model of type I are inconsistent with the experimental results. Similarly, the type II model also fails to interpret the experimental rRTN results, which is verified by the simulated RTN result shown in Fig. 5(d).
Last, the complete 4-state trap model with two metastable trap states is examined, as shown in Fig. 6(a), including one neutral metastable state (1′) and one charged metastable states (2′). Zone A corresponds to the switching process between state 1′ and state 2, and zone B is between state 1 and state 2′. It is worth mentioning that the transition probabilities of 1 → 1′ (or 2 → 2′) is usually smaller compared with other transition processes, due to higher barrier ε 11′ (or ε 2′2 ) than others. Therefore, in previously reported experiments, it is rare to observe RTN data featuring the transitions among four states. Regarding the rRTN observed in this paper, particularly, the 4-state trap model can be described in the reaction coordinate as shown in Fig. 6(b). The transition barriers should follow these relationships: ε 12′ < ε 11′ and ε 2′1 < ε 2′2 , otherwise, there is only single zone, as illustrated based on the simulated RTN results in Fig. S5 of the supplementary materials. Therefore, the switching between 1 ↔ 2′ (or, 2 ↔ 1′) are preferred rather than between 1 ↔ 1′ (or, 2 ↔ 2′). Once the trap state turns to the zone A, it will stay in this zone for a period until the state turns to 1′ via 1 (or, to 2 via 2′). Similarly, it can also stay in the zone B for a period until the trap state turn to 1 via 1′ (or, to 2′ via 2). In other words, the fast switching zones A and B can appear randomly with a lasting time longer than the average transition time, which is exactly consistent with the observed rRTN. Based on the extracted time constants, the simulated RTN result with the 4-state trap model can be obtained, as shown in Fig. 6(c), which is consistent with the rRTN experimental results. Finally, it can be concluded that the experimental results can only be explained by the 4-state trap model (with two metastable states), rather than the simple 2-state trap model (without metastable states) and the improved 3-state model (with one metastable state). In addition, as mentioned earlier, if the trap exhibits four states rather than two states, it can affect the frequency dependence of BTI reliability 15,20,21 , which is still under investigation.

Conclusion
In summary, single-trap induced rRTN with two evident zones is observed in nanoscale transistors with HfO 2 gate oxide. Based on the analysis of transition probabilities and the corresponding simulated RTN results, the abnormal transition mechanism can be explained by the complete 4-state trap model, thus directly verifying the existing of two metastable states at single-trap based on the experimental results, which is helpful for comprehensive understanding of trap-related device reliability and variability physics.