Electronic structure models of phosphorusδ-doped silicon

Abstract

We report a density-functional theory treatment of phosphorus ␦-doped silicon. Using large asymmetric unit cells with up to 800 atoms, we obtain first-principles doping potentials, band energies, and donor-electron distributions. The explicit and nonempirical description of both valence and donor electrons improves upon previous models of this system. The effects of overlapping ␦-doping potentials in smaller systems are adequately captured using a uniform band alignment shift.Delta doping describes the process in which the placement of dopant atoms is limited to a narrow plane in the host material. 1,2 This creates an approximately V-shaped doping potential in the plane-perpendicular direction, in which electron or hole carriers are trapped to form two-dimensional gases with a number of technologically useful properties. 3,4 Phosphorus ␦-doped silicon is particularly interesting for its relevance to nanoelectronic device fabrication including the possibility of quantum computers. 5-7 Various prototype Si:P devices are currently being developed 5,[8][9][10][11][12][13][14][15] in which patterned ␦-doped layers form conducting leads and gate electrodes. These developments warrant and motivate detailed theoretical studies into the baseline electronic properties of phosphorus ␦-doped silicon. A particular difficulty of this

Electronic properties ofδ-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

“…The vertical confinement of electrons by the donor potential shifts these conduction valleys into the bulk band gap region and splits their energy minima by the 1Γ/2Γ valley splitting. 32 The change to a tP supercell also folds the bands in the ±x and ±y directions. The ±0.81X and ±0.81Y valley minima of bulk Si are folded to ±0.37X and ±0.37Y respectively.…”

“…These studies used the nemo -d package, 30 which has also been applied to δ-doped Si:P quantum wires. 10,31 Complimentary DFT models of Si:P δ-layers and quantum wires have been proposed using the siesta and vasp packages, with localised atomic orbital (LAO) bases [32][33][34][35] and a planewave basis. 36 However, the applicability of these models to realistic device architectures is restricted by the N 3 scaling in calculation time associated with DFT.…”

Direct Measurement of the Band Structure of a Buried Two-Dimensional Electron Gas

“…Phosphorous δ-doping is a particularly attractive platform for fabricating scalable spin quantum bit architectures [1][2][3], compatible with current semiconductor technology. The band structure of the δ-layers that underpin these devices has been studied intensely using different theoretical methods [4][5][6][7][8][9], but it has hitherto not been possible to directly compare these predictions with experimental data. Here we report the first measurement of the electronic band structure of a δ-doped layer below the Si(001) surface by angle resolved photoemission spectroscopy (ARPES).…”

Interpretation of phase images of delta-doped layers

“…3b. The simulations will also be used to assess the consistency of an experimentally measured potential profile at a delta-doped layer with both predicted and measured values of the width of the free carrier wavefunction [29,30]. .…”