Carrier localization effects in III-N heterostructures are often studied in the frame of modified continuum-based models utilizing a single-band effective mass approximation. However, there exists no comparison between the results of a modified continuum model and atomistic calculations on the same underlying disordered energy landscape. We present a theoretical framework that establishes a connection between atomistic tight-binding theory and continuum-based electronic structure models, here a single-band effective mass approximation, and provide such a comparison for the electronic structure of (In,Ga)N quantum wells. In our approach, in principle, the effective masses are the only adjustable parameters since the confinement energy landscape is directly obtained from tight-binding theory. We find that the electronic structure calculated within effective mass approximation and the tight-binding model differ noticeably. However, at least in terms of energy eigenvalues, an improved agreement between the two methods can be achieved by adjusting the band offsets in the continuum model, enabling, therefore, a recipe for constructing a modified continuum model that gives a reasonable approximation of the tight-binding energies. Carrier localization characteristics for energetically low lying, strongly localized states differ, however, significantly from those obtained using the tight-binding model. For energetically higher lying, more delocalized states, good agreement may be achieved. Therefore, the atomistically motivated continuum-based single-band effective mass model established provides a good, computationally efficient alternative to fully atomistic investigations, at least at when targeting questions related to higher temperatures and carrier densities in (In,Ga)N systems.

中文翻译：

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铟含量不同的III族氮化物量子阱电子结构的多尺度模拟：连接基于原子和连续谱的模型

III-N异质结构中的载流子定位效应通常是在利用单频带有效质量近似的基于连续谱的改进模型的框架中进行研究的。但是，在相同的潜在无序能图上，修改后的连续谱模型的结果与原子计算之间没有比较。我们提供了一个理论框架，该框架建立了原子紧密结合理论与基于连续体的电子结构模型之间的联系，此处为单带有效质量近似，并为（In，Ga）N量子阱的电子结构提供了这种比较。在我们的方法中，原则上，有效质量是唯一可调整的参数，因为约束能量格局是直接从紧束缚理论获得的。我们发现，在有效质量近似值和紧密结合模型中计算出的电子结构明显不同。但是，至少在能量特征值方面，可以通过调整连续谱模型中的谱带偏移来实现两种方法之间的改进一致性，因此，可以构造出一种改进的连续谱模型，从而给出紧密度的合理近似值。束缚能量。能量低的，高度局部化的状态的载子定位特征与使用紧密结合模型获得的载子定位特征显着不同。对于精力充沛的高地，更分散的州，可以达成良好的协议。因此，建立的基于原子动力的连续谱单带有效质量模型提供了良好的