本文利用经典的热电子发射模型，探讨了在三维、二维和一维情况下半导体肖特基结中热电子发射电流推导的公式及其表达式的演变关系. 这些拓展的公式可以广泛应用于当前研究热点——低维半导体中的界面势垒提取和分析，并有助于促进学生对半导体知识的理解以及对相关科学研究和分析手段的融合运用.

In this paper, classical thermionic emission model is employed to explore the formulas and their evolution for derivation of thermionic emission current in semiconductor Schottky junctions under three-dimensional, two-dimensional, and one-dimensional scenarios. These extended formulas can be widely applied to current research hotspot of interface barrier extraction and analysis in low-dimensional semiconductors, and should further contribute to enhancing students' understanding of semiconductor knowledge and the integrated application of related scientific research and analytical methods.