A density-dependent two-temperature model is applied to describe laser excitation and the following relaxation processes of silicon in an external electric field. Two approaches on how to describe the effects of the external electric field are presented. The first approach avoids the buildup of internal electric fields due to charge separation by assuming ambipolar diffusion and adds an additional carrier-pair current. In the second approach, electrons and holes are treated separately to account for charge separation and the resulting shielding of the external electric field inside the material. The two approaches are compared to experimental results. Both the first approach and the experimental results show similar tendencies for optimization of laser ablation in the external electric field.