Kinetic theory of shot noise in non-degenerate diffusive conductors

摘要

We investigate current fluctuations in non-degenerate semiconductors, onlength scales intermediate between the elastic and inelastic mean free paths.We present an exact solution of the non-linear kinetic equations in the regimeof space-charge limited conduction, without resorting to the driftapproximation of previous work. By including the effects of a finite voltageand carrier density in the contact region, a quantitative agreement is obtainedwith Monte Carlo simulations by Gonz{\'a}lez et al., for a model of anenergy-independent elastic scattering rate. The shot-noise power $P$ issuppressed below the Poisson value $P_{Poisson}=2e\bar I$ (at mean current$\bar I$) by the Coulomb repulsion of the carriers. The exact suppressionfactor is close to 1/3 in a three-dimensional system, in agreement with thesimulations and with the drift approximation. Including an energy dependence ofthe scattering rate has a small effect on the suppression factor for the caseof short-range scattering by uncharged impurities or quasi-elastic scatteringby acoustic phonons. Long-range scattering by charged impurities remains anopen problem.