This paper contains the results of the detailed theoretical and simulation studies of the role of the secondary emission process on the breakdown voltage. Calculations were performed using a Particle-in-cell/Monte Carlo collisions (PIC/MCC) code with the secondary emission model adjusted to include the energy dependence of the secondary electron yield at large separations as well as the enhancement of the secondary emission coefficient in microgaps. Furthemore, in the presence of the magnetic field, the breakdown voltage has been determined taking into account the effect of both the equivalent pressure and the variation of Townsend's second coefficient in a magnetic field. The obtained simulation results clearly show that a proper choice of the secondary emission model in the PIC/MCC code may lead to a gratifying agreement with the experimental results for the breakdown voltage. The results discussed in this paper indicate that PIC/MCC code with the improved secondary emission models provides a good physical description of plasma for various gap sizes, not only in the presence of the electric field, but also under the simultanious action of both electric and magnetic fields.