Effect of long-range Coulomb interaction on shot-noise suppression in ballistic transport

Abstract

We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator selfconsistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of spacecharge effects in the structure. ͓S0163-1829͑97͒09735-X͔The phenomenon of shot noise, associated with the randomness in the flux of carriers crossing the active region of a device, has become a fundamental issue in the study of electron transport through mesoscopic devices. In particular, the possibility of shot-noise suppression has recently attracted a lot of attention, both theoretically and experimentally.1 At low frequency ͑small compared to the inverse transit time through the active region͒ the power spectral density of shot noise is given by S I ϭ␥2qI, where I is the dc current, q is the electron charge, and ␥ is the suppression factor. When the carriers crossing the active region are uncorrelated, full shot noise with ␥ϭ1 ͑Poisson statistics͒ is observed. However, correlations between carriers can reduce the shot-noise value, giving ␥Ͻ1. In real mesoscopic devices different types of mechanisms resulting in shot-noise suppression can be distinguished: ͑i͒ statistical correlations due to the Pauli exclusion principle ͑important for degenerate materials obeying Fermi statistics͒, ͑ii͒ short-range Coulomb interaction ͑electron-electron scattering͒, and ͑iii͒ long-range Coulomb interaction ͑by means of the self-consistent electric potential͒. While the first two mechanisms have been extensively discussed in solid-state literature, 1 the last one has received less attention, 2 although its role in shot-noise suppression has been known for a long time in vacuum-tube devices.3 The only exception that should be mentioned is the Coulomb blockade in resonant-tunneling devices, which can be also referred to as the last mechanism of suppression. The blockade is provided by a built-in charge inside a quantum well which redistributes the chemical potential, and prevents the incoming carriers from passing through the well, thereby resulting in carrier correlation and shot-noise suppression ͑see the experimental evidence 4 ͒. The Coulomb blockade is a consequence of long-range Coulomb interaction, and it acts under the sequential tunneling regime of carrier transport.The main objective of the present paper is to prove the importance of long-range Coulomb interaction between the carriers on the shot-noise power spectrum under the ballistic regime of electron transport. The ballistic regime is now accessible in modern mesoscopic devices like electron waveguides, quantum point contacts, etc., which have characteristic lengths of the order, or smaller, than the carrier mean free path. The current exist...

Shot noise in mesoscopic conductors

“…The suppression may be arbitrarily strong in long (but still ballistic) samples. The results are in good agreement with previous numerical studies of shot noise in the same system by González et al [266,268] and Bulashenko et al [267]. The crossover between the ballistic and diffusive behavior of the non-degenerate Fermi gas was numerically studied by González et al [268,259].…”

Shot-noise anomalies in nondegenerate elastic diffusive conductors

“…Therefore this full shot-noise regime cannot be related in any way to the presence of current saturation, as it happens in other systems like vacuum tubes 19 or ballistic nondegenerate conductors. [20][21][22] Rather, it constitutes an intrinsic property of the sample related to the diffusive transport regime of carriers ͑the same phenomenon can be observed in inelastic diffusive nondegenerate semiconductors, see below and Ref. 23͒.…”

Many-particle Monte Carlo Approach to Electron Transport

“…Reid et al, 2009, or to compute current or voltage fluctuations that need very large simulation times to obtain reasonable estimators, see Refs. Albareda, Jiménez & Oriols, 2009;Gonzalez et al, 1997;Gonzalez & Pardo, 1993;Reklaitis & Reggiani, 1999;Wordelman & Ravaioli, 2000, etc.). In this chapter, we are interested in revisiting the MC computation of an ensemble of Coulomb interacting particles in an open system (an electron device) without any of the approximations mentioned in the previous paragraphs.…”

“…Elaborated semi-classical electron transport simulators solving the time-dependent BTE within the MC technique commonly fix the potential at the borders of the simulation box equal to the external bias (i.e. Dirichlet boundary conditions) and assume ad-hoc modifications of the injection rate to achieve "local" charge neutrality (Bulashenko et al, 1998;Fischetti & Laux, 2001;Gomila et al, 2002;Gonzalez et al, 1997;Gonzalez & Pardo, 1993;Jacoboni & Lugli, 1989;Reklaitis & Reggiani, 1999;Wordelman & Ravaioli, 2000). Some works do also include analytically the series resistances of a large reservoir which can be considered an improvement over the previous boundary conditions (Babiker et al, 1996).…”