发表机构
Institute Lumière Matière, Université Claude Bernard Lyon 1; Instute of Technology, Tartu（物质与光研究所，里昂第一大学; 塔尔图技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对解析公式在热场电子发射中适用范围受限的问题，提出开源代码GETELEC-3，通过直接数值求解1D-TISE并优化算法与神经网络加速，实现快速高精度的电流密度计算。
AI 中文摘要
随着电子源尺寸的减小、采用新材料制造或性能要求的提高，热场电子发射的解析公式，即Fowler-Nordheim和Murphy-Good方程及其基于JWKB的扩展，越来越多地被应用于超出其推导条件范围的情形。我们提出了GETELEC-3，一个开源代码，用一维含时无关薛定谔方程（1D-TISE）的直接数值解替代这些解析公式。已实现多种求解1D-TISE的方法，以测试速度、鲁棒性和解的不确定性。发现Noumerov算法最快，解的不确定性低于1%，并且结合一个优化内核并行推进所有电子能量，计算电流密度的成本降至几毫秒——与JWKB评估相当。为进一步提升计算速度，特别是在复杂势垒中，我们在半经典参考对数的残差上训练了一个神经网络，它能以极小计算成本再现电流密度，误差优于0.4%。该代码适用于金属和半导体，接受任意势和态密度，并配有用户友好的界面和编译好的可执行文件，以普及严格的电子发射计算和数据分析。
英文摘要
As electron sources are reduced in size, fabricated in new materials, or pushed for performance, the analytical formulations for thermo-field electron emission, namely Fowler-Nordheim and Murphy-Good equations and their JWKB-based extensions, are increasingly applied out of the range of conditions for which they were derived. We present GETELEC-3, an open-source code that replaces them with a direct numerical solution of the one-dimensional time-independent Schrödinger equation (1D-TISE). Several methods to solve the 1D-TISE have been implemented to test for speed, robustness, and solution's uncertainty. The Noumerov algorithm is found to be quickest, with the solution uncertainty below 1%, and together with an optimised kernel that advances all electron energies in parallel, the cost of calculating the current density is reduced to a few milliseconds - comparable to the JWKB evaluation. To further boost the calculation speed, especially in complicated barriers, a neural network has been trained on the residual of the logarithm of the semiclassical reference and it reproduces the current density better than 0.4% at a fraction of the computational cost. The code is developed for metals and semiconductors, accepts arbitrary potentials and density of states, and comes with a user-friendly interface and compiled executable to democratise rigorous electron emission calculations and data analysis.
Comments14 pages, 6 figures
