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能带极值处的能态密度是研究电子行为的重点内容,因为能带极值往往位于倒空间中的高对称位置,有着重要的物理意义。然而在三维结构中,鞍点处的等能面并非闭合曲面,相关教科书的分析有的过于粗浅,只给出结论,有的则借助复杂的数学手段,推导过程繁琐。本文通过求解等能面内总的状态数和能量的关系,再对能量进行求导即可得到鞍点处的态密度。该方法较为简易,也得到了教科书中的相同结论,同时简捷的推导更有助于加深读者对这一问题的认识。
Abstract：The density of states(DOS) near energy-band extrema is an important topic in the study of electronic behavior, because these extrema often occur at high-symmetry points in reciprocal space and have significant physical implications. However, in three-dimensional systems, the constant-energy surfaces near saddle points are not closed surfaces. Some relevant textbooks provide only qualitative conclusions, whereas others rely on complicated mathematical methods and lengthy derivations. In this paper, the DOS near saddle points is derived by first establishing the relationship between the total number of states enclosed by a constantenergy surface and the energy, and then differentiating it with respect to energy. This approach is relatively simple and yields the same conclusions as those given in textbooks. The concise derivation also helps readers gain a deeper understanding of the density of states near energy-band extrema.
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基本信息:
DOI：10.27024/j.wlygc.2025.11.27.03
中图分类号:O48
引用信息:
[1]胡祖徽,貟吉军,闫虹,等.三维能带极值处态密度的简捷推导[J].物理与工程().DOI:10.27024/j.wlygc.2025.11.27.03.
基金信息:
西北工业大学2024年度校级课程建设项目(XIKC2024016)
2026-04-30
2026-04-30
2026-04-30