Shallow impurity doping is an efficient route to tailor optical and electronic features of semiconductor quantum dots (QDs). However, the effect of doping is often smeared by the size, shape, and composition inhomogeneities. In this paper, we study optical properties of almost monodispersed spherical silicon (Si) QDs that are heavily doped with boron (B) and phosphorus (P). The narrow size distribution achieved by a size-separation process enables us to extract doping-induced phenomena clearly. The degree of doping-induced shrinkage of the optical band gap is obtained in a wide size range. Comparison of the optical band gap with theoretical calculations allow us to estimate the number of active donor–acceptor pairs in a QD. Furthermore, we found that the size and detection energy dependence of the luminescence decay rate is significantly modified below a critical diameter, that is ∼5.5 nm. In the diameter range above 5.5 nm, the luminescence decay rate is distributed in a wide range depending on the detection energy even in size-purified Si QDs. The distribution may arise from that of donor–acceptor distances. On the other hand, in the diameter range below 5.5 nm the detection energy dependence of the decay rate almost disappears. In this size range, which is smaller than twice of the effective Bohr radius of B and P in bulk Si crystal, the donor–acceptor distance is not a crucial factor to determine the recombination rate.

中文翻译：

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尺寸纯化的硅量子点中的供体-受体对重组。

浅层杂质掺杂是定制半导体量子点（QD）光学和电子特征的有效途径。但是，掺杂的效果通常会被大小，形状和组成不均匀性所抹去。在本文中，我们研究了重掺杂了硼（B）和磷（P）的几乎单分散的球形硅（Si）QD的光学特性。通过尺寸分离工艺实现的窄尺寸分布使我们能够清晰地提取出掺杂引起的现象。在宽的尺寸范围内获得了掺杂引起的光学带隙的收缩程度。光学带隙与理论计算的比较使我们能够估计量子点中活跃的供体-受体对的数量。此外，我们发现，发光衰变速率的大小和检测能量依赖性在临界直径（约5.5 nm）以下显着改变。在大于5.5 nm的直径范围内，即使在尺寸纯化的Si QD中，发光衰减率也会根据检测能量在较宽的范围内分布。该分布可能来自施主-受主的距离。另一方面，在小于5.5nm的直径范围内，衰减率的检测能量依赖性几乎消失。在这个尺寸范围内，小于块状硅晶体中B和P的有效玻尔半径的两倍，施主-受主距离并不是决定复合速率的关键因素。甚至在尺寸纯化的Si QD中，发光衰减率也会根据检测能量而在较宽的范围内分布。该分布可能来自施主-受主的距离。另一方面，在小于5.5nm的直径范围内，衰减率的检测能量依赖性几乎消失。在这个尺寸范围内，小于块状硅晶体中B和P的有效玻尔半径的两倍，施主-受主距离并不是决定复合速率的关键因素。甚至在尺寸纯化的Si QD中，发光衰减率也会根据检测能量而在较宽的范围内分布。该分布可能来自施主-受主的距离。另一方面，在小于5.5nm的直径范围内，衰减率的检测能量依赖性几乎消失。在这个尺寸范围内，小于块状硅晶体中B和P的有效玻尔半径的两倍，施主-受主距离并不是决定复合速率的关键因素。