We present a time dependent numerical analysis of the entanglment created between an electron freely propagating in a 2D system and a charged particle bound to a specific site by a harmonic potential. The latter can be considered as a simplified model of a shallow impurity. The dynamics of the carrier initially bound in the harmonic potential is coupled to that of the incoming electron through a screened Coulomb interaction. The entanglement is found to depend significantly on the energy of the freely propagating particle, on the confinig energy of the harmonic potential and on the sign of the charge bound by the harmonic potential. This approach allows a quantitative estimate of the decoherence undergone by propagating carrier due to a single unelastic scattering.