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We present here a theory and a computational tool, Silicon-{\sc Qnano}, todescribe atomic scale quantum dots in Silicon. The methodology is applied tomodel dangling bond quantum dots (DBQDs) created on a passivatedH:Si-(100)-(2$\times$1) surface by removal of a Hydrogen atom. The electronicproperties of DBQD are computed by embedding it in a computational box ofSilicon atoms. The surfaces of the computational box were constructed by usingDFT as implemented in {\sc Abinit} program. The top layer was reconstructed bythe formation of Si dimers passivated with H atoms while the bottom layerremained unreconstructed and fully saturated with H atoms. The computationalbox Hamiltonian was approximated by a tight-binding (TB) Hamiltonian byexpanding the electron wave functions as a Linear Combination of AtomicOrbitals and fitting the bandstructure to {\it ab-initio} results. Theparametrized 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 surfaceresulted in a DBQD state with wave function strongly localized around the Siatom and energy in the silicon bandgap. The DBQD could be charged with zero,one and two electrons. The Coulomb matrix elements were calculated and thecharging energy of a two electron complex in a DBQD obtained.

Theory of atomic scale quantum dots in silicon: dangling bond quantum dots on silicon surface