Heat generation and transport in nanoscale semiconductor devices via Monte Carlo and hydrodynamic simulations

Abstract

PurposeThe purpose of this paper is to set up a consistent off‐equilibrium thermodynamic theory to deal with the self‐heating of electronic nano‐devices.Design/methodology/approachFrom 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.FindingsA 1D n+−n−n+ silicon diode has been simulated by using the extended HM and the ETMC simulator, confirming the general behaviour.Research limitations/implicationsThe paper's analysis is limited to the 1D case. Future researches will also consider 2D realistic devices.Originality/valueThe non‐equilibrium character of electrons and phonons has been taken into account. In previous works, this methodology was used only for equilibrium phonons.

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

“…However, this equation has represented a numerically daunting task and it has raised more problems than solutions. A numerical treatment of the Wigner equation can be dealt with deterministic schemes [1][2][3][4], Direct Simulation Monte Carlo [5][6][7][8], and it is often used to derive reduced transport models, such as quantum-hydrodynamic models [9][10][11][12].…”

Electron transport in silicon nanowires having different cross-sections

“…there are more unknowns than equations. The Maximum Entropy Principle leads to a systematic way for obtaining constitutive relations on the basis of the information theory [20], as already proved successfully in the bulk case [21][22][23][24][25], and for quantum well structures [26], [27]. Actually, in a semiconductor electrons interact with phonons describing the thermal vibrations of the ions placed at the points of the crystal lattice.…”

A Hydrodynamic Model for Silicon Nanowires Based on the Maximum Entropy Principle

“…The MEP gives a systematic way for obtaining constitutive relations on the basis of information theory [13][14][15]. Such an approach has been used in the simulation of 2D nanoscale structures [33,34] and for simulating the 3D electron transport in sub-micrometric devices, in the case in which the lattice is considered as a thermal bath with constant temperature [35][36][37][38] or when the phonons are off-equilibrium [39][40][41][42][43][44][45]. We shall assume that the electron gas is sufficiently dilute, then the entropy density can be taken as the classical limit of the expression arising in the Fermi statistics, i.e.,…”