Search for Associated Production of Z and Higgs Bosons in the $ee bb$ Final State in $p\bar{p}$ Collisions at $\sqrt{s}$=1.96 TeV

We present a search for a low mass standard model Higgs boson produced in association with a $Z$ boson decaying to two electrons at a center-of-mass energy of $\sqrt{s}=$1.96~TeV with the D0 detector at the Fermilab Tevatron collider. The search is performed in events containing one or two b-tagged jets with of order 4~fb$^{-1}$ of data. As well as the inclusion of the full data set, recent improvements to the sensitivity will be discussed.