外电场与镜像电荷对碳纳米管场致发射的影响

Effect of External Electric Field and Image Charge on Field Emission of Carbon Nanotubes

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, two parameters were introduced to describe the effect on the field emission of the deviation from the infinite metal plane and the charge non even distribution at the top of carbon nanotubes. Different weight factors were numerically simulated. The results show that the barrier structure depends on weight factors, whereas the image charge and external electric field can reduce the height and width of the surface barrier; The field, emission probability was given by the first and second full elliptic integral. Taking the field emission of carbon nanotube as an example, choosing its electron energy to be 3.50 eV, the electric field strength to be 10^3 V/μm, and the weight factor to be 10^-4, the electronic transmission coefficient is obtained to be 7.0 × 10^-14 ; if the space between the tubes is selected to be 2.5 μm, the field emission current density of the flat array can be obtained to be 43.2 A/cm^2.