栅极调制纳米线的场增强因子计算

Calculation of field enhancement factor of gated nanowire

利用悬浮球模型和镜像电荷法计算了栅极调制纳米线的顶端表面电场,给出了场发射增强因子表达式β=1/2(3.5+L/r0+W),式中L与r0分别是纳米线长度与顶端表面曲率半径,W是由栅孔半径R、阴极与栅极间距d以及纳米线自身几何参数所决定的函数.结果表明,纳米线长径比对场增强因子的影响很显著;当阴极与栅极间距较近时,场增强因子随d的增加而减小,而当栅极处于无穷远时,纳米线场增强因子的表示式变成β0=3.5+L/r0;栅孔半径越小,场增强因子就越大,当栅孔半径趋于零时,场增强因子为β=β0+1.202(L/d)3.

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/ ro ＋ W）, where L and ro 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 β = β0 ＋ 1.202（L/d）^3 when the gatehole radius tends to zero.