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This paper presents a novel framework for accurate estimation of key statistical parameters of the subthreshold-and gate-leakage distributions of a chip under parameter variations while considering both within-die and die-to-die variabilities in process (P), temperature (T), and supply voltage (V). For the first time, temperature variations and, more importantly, electrothermal couplings between junction (substrate or die) temperature and leakage power have been accounted for in a full-chip leakage estimation methodology. In the proposed framework, instead of exact leakage distribution profile, its statistically important parameters, such as nominal value and spread, are computed. Initially, at the transistor level, a quantitative analysis of the relative sensitivities of device leakage components to P-T-V variations is performed to extract a transistor-level variation model. It is shown that the proposed statistical model, as compared to others in the literature, shows better agreement with BSIM1 model-based simulations. It is also demonstrated that failing to account for temperature variations and electrothermal couplings can result in significant inaccuracy in chip-level leakage estimation. Furthermore, the full-chip leakage-power distribution is used to estimate the leakage-constrained yield under the impact of variations. The calculations show that yield is significantly lowered due to the within-die and die-to-die process and temperature variations. Subsequently, the proposed framework is applied in the leakage estimation of complex logic circuits with a consideration of spatial correlations of process parameters and transistor stacking effects.