Classical and quantum trajectory-based approaches to electron transport with full coulomb correlations

Resumen

The exact computation of a system of interacting electrons is extremely complicated because the motion of one electron depends on the positions of all others (i.e. electrons are correlated). Thus, the prediction of the collective behavior of many electrons is still a very active field of research in nano-electronics, quantum chemistry, nano-biology, quantum computing, materials science, etc. Several theoretical approximations have been proposed to improve the treatment of electron-electron correlations. The accurate treatment of the electron-electron correlations in electron devices is even a more difficult issue because we deal with non-equilibrium open systems. For classical electron transport approaches, the electrostatic interaction among electrons is commonly obtained from an explicit solution of the mean-field Poisson (Coulomb) equation. However, this does not provide an exact treatment of the classical Coulomb electron-electron correlations, but only an average estimation. The explicit consideration of the wave nature of electrons implies an additional computational burden, and the difficulties in treating the Coulomb interaction among electrons increase. Nonetheless, the mean-field approximation appears again as an improvement of electron-electron correlations. In this dissertation, a classical and quantum time-dependent many-particle approach to electron transport is developed in terms of a Hamiltonian that describes 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 are discussed in detail to include the Coulomb interaction between particles inside and outside of the open system. Classically, the solution of this time-dependent many-particle Hamiltonian is obtained via a coupled system of Newton-like equations with a different electric field for each particle. The quantum mechanical solution of this many-particle Hamiltonian is achieved using a time-dependent quantum (Bohm) trajectory algorithm. The validity of the classical and quantum electron transport approach to compute observable results such as the current density or the power consumption is explicitly demonstrated. Finally, the computational viability of the many-particle algorithms to build powerful nanoscale device simulators is demonstrated for classical and quantum electron devices. In particular, their application to simulate some interesting aspects of advanced nanoscale electron devices provides new valuable information on the role played by electron Coulomb correlations in the establishment of macroscopic characteristics such as the electrical current, power consumption, current and voltage fluctuations, etc.