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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.

Hydrodynamic‐like models are commonly used for describing carrier transport in semiconductor devices. One major problem of this formulation is how to model the production terms. In this paper the relaxation‐time approximation and the moments expansion of the production terms are checked with Monte Carlo simulations for a one dimensional n⁺ – n – n⁺ silicon diode in the spherical parabolic band approximation.

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.

To provide an accurate analysis of the systematic error introduced by the constant time technique free flight mechanism, due to the choice of the time step and number particles.

A homogeneous (bulk) silicon semiconductor is studied by using direct simulation Monte Carlo (DSMC).

The systematic error turns out to be of the first order with respect to the time step. The efficiency of the method is tackled.

The analysis is limited to the bulk case. Future researches will consider non homogeneous devices

An accurate analysis of an “old” free flight mechanism has been performed, and its limits have been stated.