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首页> 外文期刊>Journal of Physics. Condensed Matter >Curved nanowire structures and exciton binding energies
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Curved nanowire structures and exciton binding energies

机译：弯曲的纳米线结构和激子结合能

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摘要

Growth of quantum-confined semiconductor structures is a complicated process that may lead to imperfect and complex shapes as well as geometrical nonuniformities when comparing a large number of intended identical structures. On the other hand, the possibility of tuning the shape and size of nanostructures allows for extra optimization degrees when considering electronic and optical properties in various applications. This calls for a better understanding of size and shape effects. In the present work, we express the one-band Schr_dinger equation in curved coordinates convenient for determining eigenstates of curved quantum-wire and quantum-dash structures with large aspect ratios. Firstly, we use this formulation to solve the problem of single-electron and single-hole states in curved nanowires. Secondly, exciton states for the curved quantum-wire Hamiltonian problem are found by expanding exciton eigenstates on a product of single-particle eigenstates. A simple result is found for the Coulomb matrix elements of an arbitrarily curved structure as long as the radius-of-curvature is much larger than the cross-sectional dimensions. We use this general result to compute the groundstate exciton binding energy of a bent nanowire as a function of the bending radius-of-curvature. It is demonstrated that the groundstate exciton binding energy increases by 40 meV as the radius-of-curvature changes from 20 to 2 nm while keeping the total length (and volume) of the nanowire constant.
机译：量子限制的半导体结构的生长是一个复杂的过程，当比较大量预期的相同结构时，可能会导致不完美和复杂的形状以及几何上的不均匀性。另一方面，当考虑各种应用中的电子和光学特性时，调整纳米结构的形状和尺寸的可能性允许额外的优化程度。这需要更好地了解尺寸和形状效果。在目前的工作中，我们在弯曲坐标系中表达一个单带Schr_dinger方程，方便确定具有宽高比的弯曲量子线和量子点结构的本征态。首先，我们使用这种公式来解决弯曲纳米线中的单电子和单孔态问题。其次，通过在单粒子本征态的乘积上扩展激子本征态来找到弯曲量子线哈密顿问题的激子态。对于任意弯曲结构的库仑矩阵元素，只要曲率半径比横截面尺寸大得多，就会发现一个简单的结果。我们使用此一般结果来计算弯曲的纳米线的基态激子结合能，作为弯曲曲率半径的函数。结果表明，当曲率半径从20 nm变为2 nm时，基态激子结合能增加40 meV，同时保持纳米线的总长度（和体积）恒定。

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