The field enhancement is one of the important factors that indicate the performance of field emission cold cathode devices. It is intimately related to the field emission current density and the threshold voltage of the device. In our paper, the field enhancement factor of a normal-gated field emission nanowire cold cathode model was analytically deduced on the basis of classical electrostatic theory, and it is given by the equation. β=k1{N2·(L-d1)2+［1/k1+(L-d1)］2}1/2. The effect of geometrical parameters of the device on the field enhancement factor was explored. The theoretical analysis showed that the larger the length (L-d1) of nanowire above the gate and the gate hole radius, the larger the enhancement factor is; but the larger the nanowire radius, the smaller the enhancement factor is. When the L is much larger thand1, the enhancement factor satisfies the relation. β∝Ｌ／r0, for which N=N1(k1r0)/N0(k1r0), N0(k1r0) and N1(k1r0) are both Neumann functions and k1=0.8936/R. R, L, r0 and d1 are the gate hole radius, the nanowire length, the nanowire radius and the gate-cathode distance, respectively.

To estimate the field enhancement factor of the gated nanowire, the image charge model of floating sphere between parallel gate and cathode plates is proposed. The field enhancement factor of the gated nanowire is expressed by β=1/2（3.5+L/r0+W）, where L and r0 are the length and tip radius of nanowire, respectively, and W is a function of the gate-hole radius R, gate-cathode distance d and the geometrical parameters of the nanowire. The calculation results show that the influence of the aspect ratio of the nanowire on the enhancement factor is remarkable, i.e., the enhancement factor increases rapidly with the increase of the length and top curvature of the nanowire. Furthermore, the enhancement factor decreases with the increase of the gate-cathode distance and is equal to β0=3.5+L/r0 when the gate-cathode distance tends to infinite. The smaller the gate-hole radius, the larger the enhancement factor, and the enhancement factor will be equal to β=β0+1.202（L/d）3 when the gate-hole radius tends to zero.