Electronic states and wavefunctions of diatomic donor molecular ions in silicon: multi-valley envelope function theory

Klymenko, M.V.; Remacle, Françoise

doi:10.1088/0953-8984/26/6/065302

Cited by 16 publications

(19 citation statements)

References 42 publications

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“…More realistic studies exist in the literature, at the cost of treating only specific centers. For example, while we assume isotropic envelopes, a recent study [34] preserves the Si band anisotropy effects in an analysis restricted to D + 2 (one-electron donor pair ions), with which our results are in fair agreement.…”

Section: Discussionsupporting

confidence: 55%

Theory of one and two donors in silicon

Saraiva

Baena

Calderón

et al. 2015

J. Phys.: Condens. Matter

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We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D(0), D(-), D(+)(2) and D(0)(2) centers. The impact of different levels of approximation is discussed. The most accurate instances--for which we provide quantitative results--are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations--in particular, for a donor pair, we discuss the single orbital LCAO method, the Hückel approximation and the Hubbard model. Finally, we connect these results with recent experiments on devices with few dopants.

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Section: Discussionsupporting

confidence: 55%

Theory of one and two donors in silicon

Saraiva

Baena

Calderón

et al. 2015

J. Phys.: Condens. Matter

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“…in the weak coupling limit t U and t ∆ V O (where ∆ V O is the valley-orbit splitting of the order of 10 meV). This limit corresponds to inter-donor distances larger than 5 nm 34,35,71 . The tunnel coupling variations can easily be deduced from the exchange coupling variations since t min /t max = J min /J max , plotted in Fig.…”

Section: Long Distance Limitmentioning

confidence: 99%

Valley interference and spin exchange at the atomic scale in silicon

et al. 2020

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Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

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“…Of special note is that both theories agree perfectly on where the transition between the strong-and weak-coupling regimes occurs, in which the first excited state changes character. 14,16 Shown as a kink in the curves of Fig 3a, this transition occurs at about 6 nm separation along [100].…”

Section: A Exhaustive Enumeration Of Tunnel Couplingsmentioning

confidence: 99%

Multivalley effective mass theory simulation of donors in silicon

et al. 2015

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Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than spherical, donor central cell correction to accurately reproduce the experimental energy spectrum of a phosphorous impurity in silicon. We cross-validate this method against atomistic tight-binding calculations, showing that the two theories agree well for the calculation of donor-donor tunnel coupling. Further, we benchmark our results by performing a statistical uncertainty analysis, confirming that derived quantities such as the wave function profile and tunnel couplings are robust with respect to variational energy fluctuations. Finally, we apply this method to exhaustively enumerate the tunnel coupling for all donor-donor configurations within a large search volume, demonstrating conclusively that the tunnel coupling has no spatially stable regions. Though this instability is problematic for reliably coupling donor pairs for two-qubit operations, we identify specific target locations where donor qubits can be placed with scanning tunneling microscopy technology to achieve reliably large tunnel couplings.

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Electronic states and wavefunctions of diatomic donor molecular ions in silicon: multi-valley envelope function theory

Cited by 16 publications

References 42 publications

Theory of one and two donors in silicon

Theory of one and two donors in silicon

Valley interference and spin exchange at the atomic scale in silicon

Multivalley effective mass theory simulation of donors in silicon

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