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arXiv 1706.04093cond-mat.mes-hall
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半导体量子点导带有效质量方程的有限精度

Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Adam Mielnik-Pyszczorski, Krzysztof Gawarecki, Paweł Machnikowski

摘要:

有效质量方程是半导体结构中载流子态的最简单模型,它将固态系统的复杂性降低到类似薛定谔或保利方程,类似于量子力学教科书中的那些众所周知的方程。本文从八带kp理论出发,系统地推导了自组装半导体量子点在磁场中的导带有效质量方程。推导使我们能够分类的各种形式的有效质量方程的近似层次。我们评估的准确性的近似计算选定的光谱和自旋相关的特性。我们指出了保留非对角项的价带哈密顿量的重要性,并认为,有效质量理论不能达到令人满意的准确性没有自洽包括非抛物性校正和重整化的kp参数。定量比较与8带kp的结果支持的现象Roth-Lax-Zwerdling公式的g-因子的纳米结构。

英文摘要:

Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band kp theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of kp parameters. Quantitative comparison with the 8-band kp results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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