Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices

Abstract

Small semiconductor devices can be separated into regions where the electron transport has classical character, neighboring with regions where the transport requires a quantum description. The classical transport picture is associated with Boltzmann-like particles that evolve in the phase-space defined by the wave vector and real space coordinates. The evolution consists of consecutive processes of drift over Newton trajectories and scattering by phonons. In the quantum regions, a convenient description of the transport is given by the Wigner-function formalism. The latter retains most of the basic classical notions, particularly, the concepts for phase-space and distribution function, which provide the physical averages. In this work we show that the analogy between classical and Wigner transport pictures can be even closer. A particle model is associated with the Wigner-quantum transport. Particles are associated with a sign and thus become positive and negative. The sign is the only property of the particles related to the quantum information. All other aspects of their behavior resemble Boltzmann-like particles. The sign is taken into account in the evaluation of the physical averages. The sign has a physical meaning because positive and negative particles that meet in the phase space annihilate one another. The Wigner and Boltzmann transport pictures are explained in a unified way by the processes drift, scattering, generation, and recombination of positive and negative particles. The model ensures a seamless transition between the classical and quantum regions. A stochastic method is derived and applied to simulation of resonant-tunneling diodes. Our analysis shows that the method is useful if the physical quantities do not vary over several orders of magnitude inside a device.

Decoherence due to contacts in ballistic nanostructures

“…This model should hold regardless of whether the structure has resonances or not, as it is constructed to mimic the source term in the single-particle density matrix 15,16,17,18,19,20 and Wigner function 2,3,21,22,23,24,25,26,27,28,29 formalisms, and preserve the continuity of current, state-by-state. In Sec.…”

“…14 The purpose of this paper is to provide a simple description of the nonunitary evolution of a ballistic nanostructure's active region due to the injection of carriers from the contacts. Carrier injection from the contacts into the active region is traditionally described by either an explicit source term, such as in the single-particle density matrix, 15,16,17,18,19,20 Wigner function 2,3,21,22,23,24,25,26,27,28,29 and Pauli equation 30,31 transport formalisms, or via a special self-energy term in the ubiquitous nonequilibrium Green's function formalism. 32,33,34,35,36,37 In this work, the problem of contact-induced decoherence is treated using the open systems formalism: 38 we start with a model interaction Hamiltonian that describes the injection of carriers from the contacts, and then deduce the resulting nonunitary evolution of the active region's many-body reduced statistical operator in the Markovian approximation.…”

Coulomb-driven terahertz-frequency intrinsic current oscillations in a double-barrier tunneling structure

“…In this work, we consider a GaAs-based device, so the relevant scattering mechanisms are with polar optical phonons and ionized donors 28 . Well-established methods of solving the openboundary WBTE include the finite-difference approaches 13,14,29 and Monte Carlo methods 20,[30][31][32][33] . We solve Eq.…”

A Pearson Effective Potential for Monte-Carlo Simulation of Quantum Confinement Effects in nMOSFETs

“…Given the strong analogy between Wigner and Boltzmann formalisms, the Monte-Carlo method commonly used for semi-classical transport simulation can be extended to the quantum case by considering the Wigner function as an ensemble of pseudo-particles (Shifren et al, 2003 ;Nedjalkov et al, 2004 ;Querlioz et al, 2006). This approach describes well the wave-like nature of particles and has been first applied to the one-dimensional (1D) simulation of double-barrier resonant structures.…”