带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.

Study on field enhancement of a normal-gated field emission nanowire cold cathode

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.