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...
