Theory of one and two donors in silicon

Saraiva, André; Baena, Alejandra; Calderón, M. J.; Koiller, Belita

doi:10.1088/0953-8984/27/15/154208

Cited by 50 publications

(85 citation statements)

References 57 publications

(127 reference statements)

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“…[8] Notice that the phenomenological central cell has a different radius r cc for the anisotropic model of the mass compared to the spherical mass model adopted in Ref. [8]. For the anisotropic model, the radii are r cc (P) = 120 pm and r cc (As) = 128 pm for P donors and As donors, respectively.…”

Section: Modelmentioning

confidence: 97%

“…Additionally we take into account a central cell correction potential which is donor species dependent and chosen to reproduce each experimental ground state energy. [8] Notice that the phenomenological central cell has a different radius r cc for the anisotropic model of the mass compared to the spherical mass model adopted in Ref. [8].…”

Section: Modelmentioning

confidence: 99%

“…An isotropic approximation for the envelope exp(−r/a) leads to a single average Bohr radius a = 1.106 nm for P and a = 0.815 nm for As. [8] The exact value of a and b have an impact only on the size of the image, not on the details of its symmetry and oscillations. We adopt from now on a = 0.90 nm and b = 0.52 nm for the theoretical calculations (which lead to the same b/a ratio as the original KL theory but incorporates the radii reduced by the central cell).…”

Section: Modelmentioning

confidence: 99%

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Donor wave functions in Si gauged by STM images

et al. 2016

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The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wavefunctions will withstand an experimental test. Such wavefunctions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resemble a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the non-monotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001} atomic planes, including a counterintuitive reduction of the symmetry -a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wavevector to k0 = (0.82 ± 0.03)(2π/aSi). Unlike prior measurements, averaged over a sizeable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b/a. We demonstrate that the central cell corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wavefunctions as well.

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Section: Modelmentioning

confidence: 97%

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

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Donor wave functions in Si gauged by STM images

et al. 2016

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“…8 The central cell prescription discussed in Ref. 9 is incorporated in our model calculations below.…”

Section: A Single Donormentioning

confidence: 99%

“…The first approximation is to assume isotropic envelopes by taking a = b = a cc , where the subscript cc refers to the effective Bohr radius obtained from a central cell corrected potential, 9 given in table I. We do this for each of the valleys separately, preserving the conduction band six-fold degeneracy and the physical insight on valley degeneracy effects, e.g., valley interference.…”

Section: Calculation Of Lcdo Parameters -Single Vs Multi-valley mentioning

confidence: 99%

Mitigating valley-driven localization in atomically thin dopant chains in Si

Dusko¹,

Saraiva²,

Koiller³

2016

Phys. Rev. B

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We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multi-valley effective mass theory (MV-EMT). We extend this model to describe chains of donors as a linear combination of dopant orbitals. Disorder in donor positioning is taken into account, leading to an intricate disorder distribution of hoppings between nearest neighbor donor sites (donor-donor tunnel coupling) -an effect of valley interference. The localization length is obtained for phosphorous (P) donor chains from a transfer matrix approach and is further compared with the chain length. We quantitatively determine the impact of uncertainties δR in the implantation position relative to a target and also compare our results with those obtained without valley interference. We analyse systematically the aimed inter-donor separation dependence (R0) and show that fairly diluted donor chains (R0 = 7.7 nm) may be as long as 100 nm before the effective onset of Anderson localization, as long as the positioning error is under a lattice parameter (δR < 0.543 nm).

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Position‐Controlled Functionalization of Vacancies in Silicon by Single‐Ion Implanted Germanium Atoms

Achilli

Fratesi

et al. 2021

Adv Funct Materials

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Special point defects in semiconductors have been envisioned as suitable components for quantum-information technology. The identification of new deep centers in silicon that can be easily activated and controlled is a main target of the research in the field. Vacancy-related complexes are suitable to provide deep electronic levels but they are hard to control spatially. With the spirit of investigating solid state devices with intentional vacancy-related defects at controlled position, the functionalization of silicon vacancies is reported on here by implanting Ge atoms through single-ion implantation, producing Ge-vacancy (GeV) complexes. The quantum transport through an array of GeV complexes in a silicon-based transistor is investigated. By exploiting a model based on an extended Hubbard Hamiltonian derived from ab initio results, anomalous activation energy values of the thermally activated conductance of both quasi-localized and delocalized many-body states are obtained, compared to conventional dopants. Such states are identified, forming the upper Hubbard band, as responsible for the experimental sub-threshold transport across the transistor. The combination of the model with the single-ion implantation method enables future research for the engineering of GeV complexes toward the creation of spatially controllable individual defects in silicon for applications in quantum information technology.

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Theory of one and two donors in silicon

Cited by 50 publications

References 57 publications

Donor wave functions in Si gauged by STM images

Donor wave functions in Si gauged by STM images

Mitigating valley-driven localization in atomically thin dopant chains in Si

Position‐Controlled Functionalization of Vacancies in Silicon by Single‐Ion Implanted Germanium Atoms

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