In this work, we explore the optimal size of nanogaps for the high field emission (FE) efficiency. In the FE process, the emission current is highly dependent upon both the material properties and the shape of the emitter. Thus, we first calibrate the theoretical model with the experimental data using the numerical simulation which is developed to evaluate the FE efficiency under different conditions. A three-dimensional finite-difference time-domain particle-in-cell method which approaches to self- consistent simulation of the electromagnetic fields and charged particles is adopted to simulate the electron emission in the surface-conduction electron-emitter display (SED) device. Examinations into conducting characteristics, FE efficiency, local electric fields around the emitter, and current density on the anode plate with one surface conduction electron-emitter (SCE) are conducted. It is found that the optimal width of nanogap in the SCE is about 80'-'90 nm and optimal thickness of the emitter is 30 nm to obtain the highest FE efficiency. This study benefits the advanced SED design for a new type of electron sources.