High electric fields, that are characteristic of sub-micron devices, produce highly energeticelectrons, lack of equilibrium between electrons and phonons and high rates of heatgeneration. This regime can be described using an extended hydrodynamic model, which isformed by a set of conservation laws of hyperbolic-type with stiff relaxation terms. In order toovercome this numerical difficulty, an implicit–explicit Runge–Kutta scheme has been used
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