We present here a theory and a computational tool, Silicon-{\sc Qnano}, to describe atomic scale quantum dots in Silicon. The methodology is applied to model dangling bond quantum dots (DBQDs) created on a passivated H:Si-(100)-(2$\times$1) surface by removal of a Hydrogen atom. The electronic properties of DBQD are computed by embedding it in a computational box of Silicon atoms. The surfaces of the computational box were constructed by using DFT as implemented in {\sc Abinit} program. The top layer was reconstructed by the formation of Si dimers passivated with H atoms while the bottom layer remained unreconstructed and fully saturated with H atoms. The computational box Hamiltonian was approximated by a tight-binding (TB) Hamiltonian by expanding the electron wave functions as a Linear Combination of Atomic Orbitals and fitting the bandstructure to {\it ab-initio} results. The parametrized TB Hamiltonian was used to model large finite Si(100) boxes (slabs) with number of atoms exceeding present capabilities of {\it ab-initio} calculations. The removal of one hydrogen atom from the reconstructed surface resulted in a DBQD state with wave function strongly localized around the Si atom and energy in the silicon bandgap. The DBQD could be charged with zero, one and two electrons. The Coulomb matrix elements were calculated and the charging energy of a two electron complex in a DBQD obtained.

中文翻译：

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硅原子尺度量子点理论：硅表面悬空键量子点

我们在此介绍了一种理论和计算工具 Silicon-{\sc Qnano} 来描述硅中的原子级量子点。该方法应用于通过去除氢原子在钝化的 H:Si-(100)-(2$\times$1) 表面上创建的悬空键量子点 (DBQD) 模型。DBQD 的电子特性是通过将其嵌入硅原子计算盒来计算的。计算框的表面是通过使用在 {\sc Abinit} 程序中实现的 DFT 构建的。顶层通过形成被 H 原子钝化的 Si 二聚体重建，而底层保持未重建并完全被 H 原子饱和。通过将电子波函数扩展为原子轨道的线性组合并将能带结构拟合到 {\it ab-initio} 结果，计算盒哈密顿量近似为紧束缚 (TB) 哈密顿量。参数化的 TB 哈密顿量用于模拟大型有限 Si(100) 盒（板），其原子数量超过了 {\it ab-initio} 计算的当前能力。从重建表面去除一个氢原子导致 DBQD 状态，其波函数强烈地集中在 Si 原子周围，能量位于硅带隙中。DBQD 可以带零、一个和两个电子。计算库仑矩阵元素并获得 DBQD 中两个电子复合物的充电能量。参数化的 TB 哈密顿量用于模拟大型有限 Si(100) 盒（板），其原子数量超过了 {\it ab-initio} 计算的当前能力。从重建表面去除一个氢原子导致 DBQD 状态，其波函数强烈地集中在 Si 原子周围，能量位于硅带隙中。DBQD 可以带零、一个和两个电子。计算库仑矩阵元素并获得 DBQD 中两个电子复合物的充电能量。参数化的 TB 哈密顿量用于模拟大型有限 Si(100) 盒（板），其原子数量超过了 {\it ab-initio} 计算的当前能力。从重建表面去除一个氢原子导致 DBQD 状态，其波函数强烈地集中在 Si 原子周围，能量位于硅带隙中。DBQD 可以带零、一个和两个电子。计算库仑矩阵元素并获得 DBQD 中两个电子复合物的充电能量。