Thin, high-density layers of dopants in semiconductors, known as δ-layer systems, have recently attracted attention as a platform for exploration of the future quantum and classical computing when patterned in plane with atomic precision. However, there are many aspects of the conductive properties of these systems that are still unknown. Here we present an open-system quantum transport treatment to investigate the local density of electron states and the conductive properties of the δ-layer systems. A successful application of this treatment to phosphorous δ-layer in silicon both explains the origin of recently-observed shallow sub-bands and reproduces the sheet resistance values measured by different experimental groups. Further analysis reveals two main quantum-mechanical effects: 1) the existence of spatially distinct layers of free electrons with different average energies; 2) significant dependence of sheet resistance on the δ-layer thickness for a fixed sheet charge density.

半导体中薄的、高密度的掺杂层，称为δ层系统，最近作为探索未来量子和经典计算的平台而受到关注，当在平面上以原子精度进行图案化时。然而，这些系统的导电特性的许多方面仍然未知。在这里，我们提出了一种开放系统量子传输处理，以研究电子态的局部密度和δ层系统的导电特性。这种处理对磷δ的成功应用硅中的层既解释了最近观察到的浅子带的起源，又再现了不同实验组测量的薄层电阻值。进一步的分析揭示了两个主要的量子力学效应：1）存在具有不同平均能量的空间不同的自由电子层；2)对于固定的薄层电荷密度，薄层电阻对δ层厚度的显着依赖性。