Solid phase epitaxial regrowth (SPER) of p-doped preamorphized Si was studied by time resolved reflectivity. Strain and dopant concentration were opportunely varied by implanting neutral (Ge) and isovalent (B, Ga) impurities in order to disentangle the two different effects on SPER. Larger SPER rate variations occurred in strained doped Si with respect to undoped samples. The generalized Fermi level shifting model was implemented to include the role of the strain and to fit the experimental data over a large range of temperature for p- and n-type doping. We introduced a charged defect, whose energy level is independent of the dopant species.