Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon

Drumm, Daniel W.; Budi, Akin; Per, Manolo C.; Russo, Salvy P.; Hollenberg, Lloyd C. L.

doi:10.1186/1556-276x-8-111

Cited by 31 publications

(61 citation statements)

References 55 publications

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“…The rate of decay of the gradient of the potential in the z direction and the depth of the potential are sensitive to ML doping density (see Table IV), donor atom configuration 28,33 and basis set size. 36 We note that including XC effects in TB1D and DFT1D (PWO) 24 and short-range effects in DFT1D (PWO) 24 does not affect the magnitude of the valley splitting. And, that when a large basis set is used effects of basis set size become relatively minor.…”

mentioning

confidence: 82%

“…The path Γ to Y is equivalent to the path Γ to X by the four-fold symmetry of the Si(001) doping plane and therefore not shown. The path Γ to Z is affected by zone-folding 36,49 because of the height of the tP supercell in the z direction and therefore also not shown. The change from an FCC unit cell to a tP supercell projects the conduction valleys in the ±z directions to Γ.…”

Section: Analysis Of the Model For A Si:p δ-Layermentioning

confidence: 99%

“…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. Historically, the effective mass theory (EMT) has also been used to study n-type δ-doped layers in Si 37 and was recently put on a firm theoretical footing for Si:P δ-layers.…”

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confidence: 99%

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

2014

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The Thomas-Fermi-Dirac (TFD) approximation and an sp 3 d 5 s * tight binding method were used to calculate the electronic properties of a δ-doped phosphorus layer in silicon. This self-consistent model improves on the computational efficiency of "more rigorous" empirical tight binding and ab initio density functional theory models without sacrificing the accuracy of these methods. The computational efficiency of the TFD model provides improved scalability for large multi-atom simulations, such as of nanoelectronic devices that have experimental interest. We also present the first theoretically calculated electronic properties of a δ-doped phosphorus layer in germanium as an application of this TFD model.

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mentioning

confidence: 82%

Section: Analysis Of the Model For A Si:p δ-Layermentioning

confidence: 99%

mentioning

confidence: 99%

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

2014

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“…Density functional theory (DFT) calculations on δ-doped germanium are conducted by adapting the general approach previously applied to Si:P by ourselves [16][17][18] and others [19][20][21] to the specific requirements of Ge:P and Ge:As. All calculations are performed using the SIESTA software.…”

Section: Methodsmentioning

confidence: 99%

Electronic structure of phosphorus and arsenicδ-doped germanium

et al. 2013

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Density functional theory in the LDA+U approximation is used to calculate the electronic structure of germanium δ-doped with phosphorus and arsenic. We characterize the principal band minima of the two-dimensional electron gas created by δ-doping and their dependence on the dopant concentration. Populated first at low concentrations is a set of band minima at the perpendicular projection of the bulk conduction band minima at L into the (kx,ky) plane. At higher concentrations band minima at Γ and ∆ become involved. Valley splittings and effective masses are computed using an explicit-atom approach, taking into account the effects of disorder in the arrangement of dopant atoms in the δ plane.

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“…Although some of this disagreement can be attributed to geometrical effects of dopant placement which we will not explore in detail (see instead Refs. [33] and [16]), the accuracy of the description of dopant electronic structure contributes to these discrepancies. Additionally, electrically detected magnetic resonance (EDMR) [34] has called into question a theoretical picture of the scattering of electrons in a two-dimensional electron gas (2DEG) from dopants in silicon [35,36].…”

Section: Introductionmentioning

confidence: 99%

Large-scale atomistic density functional theory calculations of phosphorus-doped silicon quantum bits

2013

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We present density functional theory calculations of phosphorus dopants in bulk silicon and of several properties relating to their use as spin qubits for quantum computation. Rather than a mixed pseudopotential or a Heitler-London approach, we have used an explicit treatment for the phosphorus donor and examined the detailed electronic structure of the system as a function of the isotropic doping fraction, including lattice relaxation due to the presence of the impurity. Doping electron densities (ρ doped − ρ bulk ) and spin densities (ρ ↑ − ρ ↓ ) are examined in order to study the properties of the dopant electron as a function of the isotropic doping fraction. Doping potentials (V doped − V bulk ) are also calculated for use in calculations of the scattering cross-sections of the phosphorus dopants, which are important in the understanding of electrically detected magnetic resonance experiments. We find that the electron density around the dopant leads to non-spherical features in the doping potentials, such as trigonal lobes in the (001) plane at energy scales of +12 eV near the nucleus and of -700 meV extending away from the dopants. These features are generally neglected in effective mass theory and will affect the coupling between the donor electron and the phosphorus nucleus. Our density functional calculations reveal detail in the densities and potentials of the dopants which are not evident in calculations that do not include explicit treatment of the phosphorus donor atom and relaxation of the crystal lattice. These details can also be used to parameterize tight-binding models for simulation of large-scale devices.

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Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon

Cited by 31 publications

References 55 publications

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

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

Electronic structure of phosphorus and arsenicδ-doped germanium

Large-scale atomistic density functional theory calculations of phosphorus-doped silicon quantum bits

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