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在Fowler-Nordheim理论基础上,首先,引入两个参数α和β描述碳纳米管与无限大金属平面的偏离以及碳纳米管尖端电荷分布不均匀性等因数对场致发射的影响,并对不同的权重因子η1=β/α进行了数值分析。结果表明,势垒结构与η1有关,而镜像电荷和外电场可以使表面势垒高度降低,宽度变窄。其次,用第一类和第二类全椭圆积分严格地给出了场致发射几率。以碳纳米管场致发射为例,选择电子能量为-3.50eV,外场强度为103 V/μm,权重因子为10-4,可得电子穿透系数为7.0×10-14;选择管间距为2.5μm,可得平板阵列场致发射电流密度为43.2A/cm2。
Based on the Fowler-Nordheim theory, firstly, two parameters α and β are introduced to describe the influence of the factors such as the deviation of the carbon nanotube from the infinite metal plane and the uneven distribution of the tip charge distribution of the carbon nanotube on the field emission. The weight factor η1 = β / α was analyzed numerically. The results show that the barrier structure is related to η1, while the image charge and external electric field can reduce the surface barrier height and narrow the width. Second, the field emission probability is given strictly by the first and second kind of full elliptic integrals. Take the field emission of carbon nanotubes as an example, the selected electron energy is -3.50eV, the field intensity is 103 V / μm, the weight factor is 10-4, the electron transmissivity is 7.0 × 10-14; 2.5μm, available plate array field emission current density of 43.2A / cm2.