用有限元方法计算X光源场发射阴极电流

Calculation of field-emission for miniature X-ray source with finite element method

针对场致发射阵列建立了有效的三维有限元模型来分析单个尖锥的发射电流。考虑到场致发射阵列的周期性和尖锥的轴对称性,仅对一个尖锥单元的1/4进行分析。对模型的表面施加电压边界条件,计算得到尖锥表面电场强度分布,电场强度在尖锥顶点最强,场发射电流在此处也最强。由Fowler Nordheim函数可得到尖锥表面的场致发射电流密度分布,对整个尖锥表面进行积分后得到了单个尖锥的场致发射电流约为7μA。计算了在100V门电压下不同顶端半径的场致发射电流。结果显示,场发射对顶端半径有很强的依赖性。计算了100个顶端半径为8nm的尖锥在不同门电压下的总场致发射电流,发射电流与开启电压与实际测量值符合得很好。

An effective 3-D finite element model was constructed for the field emission array to analyse the field emission current over a single tip. Considering the periodicity of field emission array and the axial symmetry of the single tip model, only 1/4 of the single tip model was analyzed. The electric field intensity distribution over the tip surface was established through calculation with appropriate voltage boundary condition applied, and it was found that the electric field intensity was the strongest at the apex of the tip, and the field emission current was also the strongest there. The field emission current density distribution over the tip surface was established using Fowler-Nordheim function, and the emission current over the single tip established by integrating the current density all over the single tip surface was 7 μA. Field emission currents were calculated for different apex radii at the gate voltage of 100V, and the results indicated that the field emission largely depends on the apex radius. Total field emission currents were calculated for 100 tips with an apex radius of 8 nm at different gate voltages, and the results indicated that both emission currents and opening voltages were in very good agreement with actual measurements.