Many-particle Hamiltonian for open systems with full Coulomb interaction: Application to classical and quantum time-dependent simulations of nanoscale electron devices

G. Albareda, J. Suñé, and X. Oriols
Phys. Rev. B 79, 075315 – Published 17 February 2009

Abstract

A many-particle Hamiltonian for a set of particles with Coulomb interaction inside an open system is described without any perturbative or mean-field approximation. The boundary conditions of the Hamiltonian on the borders of the open system [in the real three-dimensional (3D) space representation] are discussed in detail to include the Coulomb interaction between particles inside and outside of the open system. The many-particle Hamiltonian provides the same electrostatic description obtained from the image-charge method, but it has the fundamental advantage that it can be directly implemented into realistic (classical or quantum) electron device simulators via a 3D Poisson solver. Classically, the solution of this many-particle Hamiltonian is obtained via a coupled system of Newton-type equations with a different electric field for each particle. The quantum-mechanical solution of this many-particle Hamiltonian is achieved using the quantum (Bohm) trajectory algorithm [X. Oriols, Phys. Rev. Lett. 98, 066803 (2007)]. The computational viability of the many-particle algorithms to build powerful nanoscale device simulators is explicitly demonstrated for a (classical) double-gate field-effect transistor and a (quantum) resonant tunneling diode. The numerical results are compared with those computed from time-dependent mean-field algorithms showing important quantitative differences.

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  • Received 12 July 2008

DOI:https://doi.org/10.1103/PhysRevB.79.075315

©2009 American Physical Society

Authors & Affiliations

G. Albareda, J. Suñé, and X. Oriols*

  • Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

  • *Corresponding author: xavier.oriols@uab.es

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Issue

Vol. 79, Iss. 7 — 15 February 2009

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