利用静电学和测量数据对碳纳米管膜场致发射规律的定量分析

Quantitative Analysis of the Field Emission of Carbon-Nanotube Film Based on Electrostatics and Experimental Measurement Data

碳纳米管膜的场致发射电流密度仅由它表面的宏观电场决定,无论其表面形状是平的还是半球状的。对于理想的平行板电极系统,其表面电场强度均匀(U/d),发射电流密度、总电流与发射面积成正比;对于半球平面电极系统半球形的阴极存在一个宏观场增强因子ks,一个与两极距离和球半径之比(d/r)相关的函数,其表面的平均场强为ksU/d。对于d/r=0,ks=1,d r的情况,ks接近于常数。对于10<d/r<100的情况,存在一个经验的表达式:ks=1+0.15d/r-0.005(d/r)2。在引入ks后,不同作者给出的平面电极系统和半球平面电极系统碳纳米管膜的场致发射电流I与宏观表面电场强度E的关系都可以近似用一经验公式描述:I=a(E-Eo)b,a,b为常数。该经验公式可为稳定生产的CNT膜片应用产品设计提供方便。

The field emission current density of any a CNT film is determined only by local macroscopic surface electric field, no matter the surface shape is plane or hemisphere. In an ideal parallel plane electrode system, where field intensity is uniform （ = U/d） among the CNT surface and so is emission current density, total current is proportional to total emission area. When cathode is hemispherical, a macroscopic field enhancement factor ks, which is a function of d/r （ratio of electrode distance to radius of hemisphere）, makes surface average intensity be ksU/d. When d/r = 0, ks= 1. d ≥ r, ks is near to a constant. An empirical expressions for 10 〈 d/r 〈 100 is ks =- 1 ＋ 0.15d/r - 0.005（d/r）^2. The intrinsically determined β of a CNT film is independent of d and U. Empirical equations between current and field intensity can be found for any a type of CNT firm from measured data. Typical one is a power function as I =： a （E - Eo）^b with properly Eo choosen.