Self-consistent theory of current and voltage noise in multimode ballistic conductors

Abstract

Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a threedimensional Fermi-Dirac injection has been analyzed. We show that the Coulomb correlations are manifested in the negative excess voltage noise, i.e., the voltage fluctuations under high-field transport conditions can be less than in equilibrium.

Shot-noise spectroscopy of energy-resolved ballistic currents

“…In a semiclassical framework, the electron occupation numbers f (x,k ជ ,t) are determined by the electron flows from the left and right leads. 9 FIG. 1.…”

“…͑6͒ and ͑9͒ imply that the width of the peak is narrow on the scale of the temperature T. The addition of extra peak electrons bring the injection away from equilibrium. Therefore one cannot use the thermal-equilibrium Nyquist relationship 9 for the injected electrons.…”

“…9 The ␦ functions in Eqs. ͑6͒ and ͑9͒ imply that the width of the peak is narrow on the scale of the temperature T. The addition of extra peak electrons bring the injection away from equilibrium.…”

“…Assuming that the barrier is much wider than the wavelength of electrons, one can neglect tunneling and quantum reflection, i.e., the transmission probability is 1 if the electron energy is higher than the barrier height, and it is 0 in the opposite case. In this framework, the transport is described by the collisionless Boltzmann equation selfconsistently coupled with the Poisson equation supplemented by the stochastic boundary conditions for the occupation numbers: 8,9 ͩ ‫ץ‬…”

“…As was recently shown, Coulomb interactions may suppress the shot noise down to several orders of magnitude in spacecharge-limited ballistic conductors. 8,9 In this paper, we focus mainly on the question of how the effect of Coulomb interactions on the shot noise can be employed to reveal important information on the energy profile of nonequilibrium carriers injected from an emitter contact.…”