  Aims. The aim of this work is to study the contribution of the Ly-a emitters
(LAE) to the star formation rate density (SFRD) of the Universe in the interval
2<z<6.6.
  Methods. We assembled a sample of 217 LAE from the Vimos-VLT Deep Survey
(VVDS) with secure spectroscopic redshifts in the redshift range 2 < z < 6.62
and fluxes down to F=1.5x10^18 erg/s/cm^2. 133 LAE are serendipitous
identifications in the 22 arcmin^2 total slit area surveyed with the VVDS-Deep
and the 3.3 arcmin^2 from the VVDS Ultra-Deep survey, and 84 are targeted
identifications in the 0.62 deg^2 surveyed with the VVDS-DEEP and 0.16 deg^2
from the Ultra-Deep survey. Among the serendipitous targets we estimate that
90% of the emission lines are most probably Ly-a, while the remaining 10% could
be either [OII]3727 or Ly-a. We computed the LF and derived the SFRD from LAE
at these redshifts.
  Results. The VVDS-LAE sample reaches faint line fluxes F(Lya) = 1.5x1^18
erg/s/cm^2 (corresponding to L(Lya)=10^41 erg/s at z~3) enabling the faint end
slope of the luminosity function to be constrained to a=-1.6+-0.12 at redshift
z~2.5 and to a=-1.78+0.1-0.12 at z=4, placing on firm statistical grounds
trends found in previous LAE studies, and indicating that sub-L* LAE contribute
significantly to the SFRD. The projected number density and volume density of
faint LAE in 2<z<6.6 with F>1.5x10^18 erg/s/cm^2 are 33 galaxies/arcmin^2 and
4x10^-2 Mpc^-3, respectively. We find that the the observed luminosity function
of LAE does not evolve from z=2 to z=6. This implies that, after correction for
the redshift-dependent IGM absorption, the intrinsic LF must have evolved
significantly over 3 Gyr. The SFRD from LAE contributes to about 20% of the
SFRD at z =2-3, while the LAE appear to be the dominant source of star
formation producing ionizing photons in the early universe z>5-6, becoming
equivalent to that of Lyman Break galaxies.
