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