Shot-Noise in Non-Degenerate Semiconductors with Energy-Dependent Elastic Scattering

Abstract

Abstract. We investigale current fluctuations in non-degenerate Semiconductors, on length scales intermediate between t he elastic and inelastic mean free paths. The shot-noise power P is suppressed below the Poisson value Ppoiasoa -2e7 (afc mean current 7) by the Coulomb repulsion of the carriers. We consider a power-law depenclence of the elastic scattering time τ oc ε α on kinetic energy ε and present an exact solution of the non-linear kinetic equations in the regime of space-charge limited conduction. The ratio P/Ppoisson decreases from 0.38 to 0 in the ränge -£ < a < 1.

Shot noise in mesoscopic conductors

“…An analytic theory of shot noise in these conductors was proposed by Beenakker [260], and subsequently by Nagaev [261] and Schomerus, Mishchenko, and Beenakker [262,263]. The general conclusion is as follows.…”

“…Furthermore, they do depend on the disorder, and this dependence enters through their sensitivity to the energy dependence of the relaxation time 60 , as noticed by Nagaev [261]. Schomerus, Mishchenko, and Beenakker [263] investigated the case τ (E) ∝ E α , −1/2 ≤ α ≤ 1, which are the only values of α compatible with the regime of space-charge limited conduction. In particular, α = −1/2 corresponds to scattering on short-ranged impurities.…”

Sub-Poissonian Shot Noise in Nondegenerate Diffusive Conductors

“…This would change the energy dependence of the diffusion constant from D ∝ ε to D ∝ ε 2−d/2 . The shot-noise power remains unaffected for d = 2, but for d = 3 one obtains [12] P/P Poisson = 0.407 -some 20% above the value for an ε-independent scattering rate. Concerning the experimental observability, the main obstacle is the tendency of electron-phonon scattering to equilibrate the electron gas at the lattice temperature.…”

The role of boundary conditions in shot noise in elastic diffusive conductors

“…In the latter case (γ in,φ negative), the values of γ depend on the competition between the diagonal and the off-diagonal contributions. For nondegenerate systems (for which γ in = 1), the presence of diagonal and off-diagonal terms explains the actual scenario taken by the Fano factor, which, according to the dimensionality in momentum space and the energy dependence of the relaxation time, was found to run from suppressed to enhanced values [15,16,18,19,22]. In contrast, for degenerate systems these effects have not been investigated to our knowledge.…”

“…The presence of electron-electron scattering was found to provide a √ 3/4 suppression factor [13,14]. Also, nondegenerate mesoscopic conductors were found to exhibit shot-noise suppression due to the presence of long-range Coulomb interactions, and a suppression factor of 1 3 , or very near to this value, was predicted by Monte Carlo calculations [15] and interpreted analytically [16][17][18]. In particular, the dimensionality in momentum space [15][16][17]19] and an energy-dependent scattering time [16,17,[19][20][21][22] were found to give different suppression values, thus washing out the universality features of suppression.…”