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The iteration approach consists of applying Numerical Monte Carlo methods for calculation of linear functional of iterated functions to an integral form of the Boltz‐mann Equation. It has been successfully used for the time‐dependent homogeneous case. The same approach, we present in this paper, can be applied for the inhomo‐geneous case, important from practical point of view. Application of the iteration approach in the particular case of obtaining the Ensemble Monte Carlo algorithm is shown.

A Monte Carlo (MC) technique useful for calculation of the high energy tail of the distribution function (d.f) is proposed. The well known MC technique for simulation in rarely visited region splits the real history of the particle, that has entered in this region, in N subhystories with weights 1/N. But the lucky event for entering must be waited to happen during the simulation. A presentation of the d.f is found here, which allows, knowing the d.f in the low (common) energy region, to simulate only high energy events. This technique can be used for example when gate current in submicrometer MOS devices is calculated.

The purpose of this paper is to deal with the self-heating of semiconductor nano-devices.

Transport in silicon semiconductor devices can be described using the Drift-Diffusion model, and Direct Simulation Monte Carlo (MC) of the Boltzmann Transport Equation.

A new estimator of the heat generation rate to be used in MC simulations has been found.

The new estimator for the heat generation rate has better approximation properties due to reduced statistical fluctuations.

The purpose of this paper is to set up a consistent off‐equilibrium thermodynamic theory to deal with the self‐heating of electronic nano‐devices.

From the Bloch‐Boltzmann‐Peierls kinetic equations for the coupled system formed by electrons and phonons, an extended hydrodynamic model (HM) has been obtained on the basis of the maximum entropy principle. An electrothermal Monte Carlo (ETMC) simulator has been developed to check the above thermodynamic model.

A 1D n⁺−n−n⁺ silicon diode has been simulated by using the extended HM and the ETMC simulator, confirming the general behaviour.

The paper's analysis is limited to the 1D case. Future researches will also consider 2D realistic devices.

The non‐equilibrium character of electrons and phonons has been taken into account. In previous works, this methodology was used only for equilibrium phonons.