We introduce a new method to analyze the statistical properties of the defects responsible for the ubiquitous recovery behavior following negative bias temperature stress, which we term time dependent defect spectroscopy (TDDS). The TDDS relies on small-area metaloxide-semiconductor field effect transistors (MOSFETs) where recovery proceeds in discrete steps. Contrary to techniques for the analysis of random telegraph noise (RTN), which only allow to monitor the defect behavior in a rather narrow window, the TDDS can be used to study the capture and emission times of the defects over an extremely wide range. We demonstrate that the recoverable component of NBTI is due to thermally activated hole capture and emission in individual defects with a very wide distribution of time constants, consistent with nonradiative multiphonon theory previously applied to the analysis of RTN. The defects responsible for this process show a number of peculiar features similar to anomalous RTN previously observed in nMOS transistors. A quantitative model is suggested which can explain the bias as well as the temperature dependence of the characteristic time constants. Furthermore, it is shown how the new model naturally explains the various abnormalities observed.

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Despite a number of recent advances made in the understanding of the bias temperature instability (BTI), there is still no simple model available which can capture BTI degradation during DC or duty-factor (DF) dependent stress and the following recovery. By exploiting the intuitive features of the recently proposed capture/emission time (CET) maps [1,2], we suggest an analytic model capable of handling a wide number of BTI stress and recovery patterns. As the model captures both the temperature-and bias-dependence of the degradation, it allows for realistic lifetime extrapolation. Compared to available models which do not consider the saturation of the degradation, our model predicts considerably more optimistic lifetimes.Introduction At the heart of the model stand the CET maps, which describe the wide distribution of capture and emission times. The CET maps have so far been extracted by numerically differentiating a set of ΔV th recovery curves [1]. It has been shown that this approach can explain a wide class of both NBTI [2] as well as PBTI [3] stress and recovery patterns, including DC, AC, and DF stress. Although accurate, such a table-based model is valid for a single stress/recovery voltage/temperature combination only, becomes prone to numerical errors at lower stress conditions, and does not allow for extrapolation. In a first attempt to overcome these limitations, a log-normal distribution with higher-order polynomials for the mean and variance for the emission times was used [2], which is unfortunately at odds with physical models.Analytic Capture/Emission Time Map Model We base our CET map model on the capture and emission times as described by the non-radiative multiphonon model for charge exchange [4], with time-constants of the form τ = τ 0 exp(β E A ). Rather than considering the various defect parameters impacting E A , like the Huang-Rhys factor or the energy levels of the trap, we deal with the effective activation energy E A directly. We consider the following: (i) Since both capture and emission are thermally activated processes [1, 4], we model the distribution of the activation energies rather than the time constants themselves. (ii) As the time constants are uncorrelated with the depth of the defect into the oxide [5], we use an effective prefactor ⟨τ 0 ⟩. (iii) Recent results have shown that BTI degradation consists of a recoverable component R which dominates the recovery over the whole experimental window, starting from a microsecond up to weeks [6]. Furthermore, a more permanent component P is observed, which is not fully permanent but merely recovers on timescales outside usual experimental windows [6]. By heating the sample, these time constants are dramatically reduced, leading to accelerated recovery also of P [7,8]. Since in physical models the capture and emission times are correlated [9], we express the mean of the emission time as μ e = μ c +Δμ e . As such, both components can be described by regular bivariate normal distributions, see Fig. 1. (iv) While the temperature depend...

We introduce the time-dependent defect spectroscopy ͑TDDS͒ for the analysis of a particular class of oxide defects known as "border traps." These defects have a fundamental impact on the behavior of metal-oxidesemiconductor field-effect transistors and are commonly linked to the occurrence of random-telegraph noise, 1 / f noise, and slow charging transients. The TDDS naturally extends the successful deep-level transient spectroscopy as it extracts both the capture and emission time constants. Analysis proceeds via the so-called spectral maps, which separate individual border traps by their characteristic times and their voltage step height. In contrast to standard random-telegraph noise analysis methods, where uncorrelated capture and emission events of only a few traps can already create convoluted noise patterns, the synchronization by the charging pulse yields the spectral maps, which allow for the analysis of a large number of defect occupancies in a single measurement. As a consequence, the TDDS allows us to monitor the defect parameters over exceptionally wide temperature and bias ranges.

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