场发射电流密度的高阶曲率修正
Higher order curvature corrections to the field emission current density
摘要：
利用二阶曲率修正的隧穿势，得到了伽莫夫因子的简单表达式。我们的研究结果表明，它近似准确的“精确WKB”的传输系数通过数值积分的隧道区域，以获得伽莫夫因子。在功函数$ϕ\in [3-5.5]$ eV、费米能量${\cal{E}}_F$（[5-10]eV）、局部电场$E_l$（[3-9]eV）和曲率半径（$R \geq 5$ nm）的范围内，使用相应的透射系数的电流密度的平均差约为$1.5 \%$。还提供了易于使用的校正因子$λ_P$，以将“精确WKB”电流密度近似映射到以${\cal{E}}_F/ϕ$表示的“精确”电流密度。发现使用$λ_P$的平均误差在$3.5\%$左右。当$15\%$。最后，使用伽莫夫因子得到曲率校正电流密度的解析表达式。它被发现比较以及与“精确WKB”的电流密度，即使在小的值的局部电场和曲率半径。
英文摘要：
A simple expression for the Gamow factor is obtained using a second order curvature corrected tunneling potential. Our results show that it approximates accurately the `exact-WKB' transmission coefficient obtained by numerically integrating over the tunneling region to obtain the Gamow factor. The average difference in current density using the respective transmission coefficients is about $1.5 \%$, across a range of work-functions $ϕ\in [3-5.5]$eV, Fermi energy ${\cal{E}}_F$ in [5-10]eV, local electric fields $E_l$ in[3-9]eV and radius of curvature $R \geq 5$nm). An easy-to-use correction factor $λ_P$ is also provided to approximately map the `exact-WKB' current density to the `exact' current density in terms of ${\cal{E}}_F/ϕ$. The average error on using $λ_P$ is found to be around $3.5\%$. This is a vast improvement over the average error of $15\%$ when $λ_P = 1$. Finally, an analytical expression for the curvature-corrected current density is obtained using the Gamow factor. It is found to compare well with the `exact-WKB' current density even at small values of local electric field and radius of curvature.
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