Mielnik-Pyszczorski Adam, Gawarecki Krzysztof, Machnikowski Paweł
Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370, Wrocław, Poland.
Sci Rep. 2018 Feb 13;8(1):2873. doi: 10.1038/s41598-018-21043-3.
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 k · p 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 k · p parameters. Quantitative comparison with the 8-band k · p results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.
有效质量方程是半导体结构中载流子态最简单的模型，它将固态系统的复杂性简化为类似于薛定谔方程或泡利方程的形式，类似于量子力学教科书中熟知的方程。在此，我们从八能带k·p理论出发，系统推导了磁场中自组装半导体量子点的导带有效质量方程。该推导使我们能够根据近似层次对有效质量方程的各种形式进行分类。我们评估了这些近似在计算选定的光谱和自旋相关特性时的准确性。我们指出了保留价带哈密顿量非对角项的重要性，并认为有效质量理论如果不包括非抛物线修正和k·p参数的自洽重整化，就无法达到令人满意的精度。与八能带k·p结果的定量比较支持了纳米结构中g因子的唯象Roth-Lax-Zwerdling公式。
