曲率校正场发射电流的快速准确测定
Fast and accurate determination of the curvature-corrected field emission current
摘要：
曲率校正的场发射电流密度，通过线性化或低于费米能量，进行了研究。两种特殊情况下，相应的正态能量分布的峰值和平均正态能量，被认为是。发现对于具有功函数$ϕ= 4.5$ eV的发射器，使用平均法向能量评估的电流密度导致对于顶点曲率半径$R_a \geq 5$ nm和对于顶点场$E_a$在$3-10$ V/nm范围内的净发射电流的误差低于3%。对于局部抛物型尖端，利用广义余弦定律也得到了净场发射电流的解析表达式。误差被发现是低于6%的$R_a \geq 5$ nm在一个相同的范围内的顶点场强。基准电流通过对发射极表面上的电流密度进行数值积分而获得，并且电流密度本身通过使用WKB透射系数的精确伽莫夫因子和肯布尔形式对能量状态进行积分而计算。的解析表达式的结果在一个显着的加速计算的净发射电流，是特别有用的大面积场发射体具有数万个发射站点。
英文摘要：
The curvature-corrected field emission current density, obtained by linearizing at or below the Fermi energy, is investigated. Two special cases, corresponding to the peak of the normal energy distribution and the mean normal energy, are considered. It is found that the current density evaluated using the mean normal energy results in errors in the net emission current below 3% for apex radius of curvature, $R_a \geq 5$nm and for apex fields $E_a$ in the range $3-10$ V/nm for an emitter having work-function $ϕ= 4.5$eV. An analytical expression for the net field emission current is also obtained for locally parabolic tips using the generalized cosine law. The errors are found to be below 6% for $R_a \geq 5$nm over an identical range of apex field strengths. The benchmark current is obtained by numerically integrating the current density over the emitter surface and the current density itself computed by integrating over the energy states using the exact Gamow factor and the Kemble form for the WKB transmission coefficient. The analytical expression results in a remarkable speed-up in the computation of the net emission current and is especially useful for large area field emitters having tens of thousands of emission sites.
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