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This letter presents a phenomenological relationship between the energy distribution of stress-induced hole traps and the power-law time exponent of NBTI. Experimental results show that increased generation of deep-level hole traps (DLHTs), i.e., trap-energy levels are near and/or above the Si conduction-band edge, yields a small exponent (< 0.2). Annealing the DLHTs results in the exponent increasing to ~ 0.3. Measurement on the n-MOSFET (in which the effect of DLHTs is suppressed) shows an exponent of ~0.4-0.5 for interface-state generation. This implies that the relatively small exponent (~0.3) of the p-MOSFET is due to remnant DLHTs which charge-up positively again when subjected to negative gate biasing during measurement. This new insight calls for a reexamination of the notion that as-measured exponents of ~0.14-0.17 are experimental proof of H2-diffusion-driven interface-state generation.