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In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are addressed in simulation.