Multivalley effective mass theory simulation of donors in silicon

Abstract

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 phosphorus 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.

10 pages, 4 figures, 3 supplemental data files

References in corpus (10)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Spatially Resolving Valley Quantum Interference of a Donor in Silicon
• Single-shot readout and relaxation of singlet/triplet states in exchange-coupled ${}^{31}$P electron spins in silicon
• Theory of one and two donors in Silicon
• Hyperfine Stark effect of shallow donors in silicon
• An Exchange-Coupled Donor Molecule in Silicon
• Phosphorus donors in highly strained silicon
• Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy
• Conduction band tight-binding description for silicon applied to phosphorous donors
• Impact of the valley degree of freedom on the control of donor electrons near a Si/SiO_2 interface

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