Electric field reduced charging energies and two-electron bound excited states of single donors in silicon

Rahman, Rajib; Lansbergen, G. P.; Verduijn, J.; Tettamanzi, G. C.; Park, S.H.; Collaert, N.; Biesemans, S.; Klimeck, Gerhard; Hollenberg, Lloyd C. L.; Rogge, Sven

doi:10.1103/physrevb.84.115428

Cited by 31 publications

(35 citation statements)

References 53 publications

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“…Simple electrostatic arguments for tip-induced band bending were employed 51 , identical to those describing metal-oxide-semiconductor capacitors. We find that the D 0 state is measured in a regime E z = (−0.3±1.9) MV/m, well below the field ∼ 20 MV/m theoretically predicted to contribute to coherent valley de-population for an arsenic donor ∼ 3 nm from an interface 52 . These electrostatic arguments were independently validated by extracting the vacuum tunneling barrier energy 37,53,54 from measured variation dI/dz in the tunnel current I with tip height z in Figure A.…”

Section: Electric Field Experienced By Donormentioning

confidence: 94%

Spatially resolving valley quantum interference of a donor in silicon

Salfi¹,

Mol²,

Rahman³

et al. 2014

Nature Mater

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105

187

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Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunctions, preventing direct experimental access to valley population, donor position, and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunneling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley perturbation-induced enhancement of spin relaxation will be negligible for depths > 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest to emerging schemes proposing to encode information directly in valley polarization. Fabrication of devices1,2 , spin readout 1 , and quantum control of spins 3,4 in silicon has been accomplished at the single-donor level. However, addressable control and coupling within qubit arrays requires local gates and control interfaces, whose atomic-scale potentials strongly influence electronic valley degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16] . While these unconventional orbital degrees of freedom play no role in conventional silicon microelectronics, they invariably arise in quantized states in indirect gap materials, and are pervasive in quantum electronics. In silicon, valley physics determines qubit relaxation rates 13,17,18 and are predicted to strongly influence two qubit gates Here, individual states of subsurface donors were measured using cryogenic scanning tunneling spectroscopy. Quantum mechanical valley interference patterns were observed in real space, associated with linear quantum superpositions of wavevectors in the six conduction band valleys of silicon. Enabled by high-accuracy empirical determination of donor depth and electric field, we perform a parameter-free comparison with atomistic theory establishing that the z-valley population is ∼ 38 ± 2% for a 2.85 ± 0.45 nm deep donor, perturbed by only ∼ 5% compared with ∼ 33.3% for a donor in bulk silicon. Consequently, donors more than 3 nm deep should not experience a significant valley-repopulation induced increase in spin-lattice relaxation. Moreover, the nearly bulklike valley interference observed will render two-qubit excha...

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Section: Electric Field Experienced By Donormentioning

confidence: 94%

Spatially resolving valley quantum interference of a donor in silicon

Salfi¹,

Mol²,

Rahman³

et al. 2014

Nature Mater

Self Cite

105

187

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“…26) compared with the 44-meV experimental value. 27 The method is described in detail in Supplementary Information.…”

Section: Methodsmentioning

confidence: 99%

“…26) compared with the 44-meV experimental value. 27 The method is described in detail in Supplementary Information.The FCI technique is an exact way to solve the multi-electron problem only limited by the number of one-electron basis functions used. The method diagonalises the multi-electron Hamiltonian in the basis of all Slater determinants constructed from the single-electron states of the system.…”

mentioning

confidence: 99%

Highly tunable exchange in donor qubits in silicon

et al. 2016

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In this article we have investigated the electrical control of the exchange coupling (J) between donor-bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We found that the asymmetric 2P-1P system provides a highly tunable exchange curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange coupling can be achieved using a modest range of electric field (3 MV/m) for~15-nm qubit separation. Compared with the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the gate density by a factor of~2. By combining large-scale atomistic tight-binding method with a full configuration interaction technique, we captured the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P-1P and 2P-1P qubits.npj Quantum Information (2016) 2, 16008; doi:10.1038/npjqi.2016.8; published online 12 April 2016 INTRODUCTION Donor qubits in silicon are promising candidates for spin-based quantum computation as they have exceptionally long T 1 (refs 1-3) and T 2 times 4-6 and offer both electron and nuclear spins for encoding quantum information 5-8 utilising commonly used silicon device technology. With recent demonstration of single qubits in silicon with both electronic and nuclear spins of donors, 5,7 the next biggest challenge is to demonstrate two-qubit gates based on the exchange interaction. Ideally, the exchange coupling J in a two-qubit gate needs to be tuned electrically by several orders of magnitude between an 'Off' and an 'On' state within a small and realisable bias range. To achieve this, the popular Kane architecture uses a J-gate between two phosphorus donors to tune the J-coupling. Recently A-gates that tune the hyperfine interaction for individual qubits have been demonstrated. 9 However, in the long run such a J-and A-gate architecture leads to a high gate density, requiring ultra-small gate widths to minimise electrical cross-talk between gates, and precise donor positioning relative to gates. Moreover, the tunability of the exchange coupling is limited both by the electric field range the J-gate can produce and by the field ionisation of the electrons to the surface. Previous calculations have also shown that the J-coupling oscillates as a function of donor separation due to crystal momentum states, 10 and is therefore sensitive to atomic-scale placement errors. All these issues lead to severe constraints in the implementation of a two-qubit gate in donors.In this work, we introduce an alternative design for an exchange gate in a two-qubit donor system, which allows flexibility in device fabrication and in tuning the exchange coupling. In principle, this new design can (1) eliminate the need for additional J-gates between the donors, (2) function with a range of donor separations, (3) provide an~5 orders of magnitude J-tunability within a modest E-field range of~3 MV/m and lowered 'Off' state exchange and (4) mitigate th...

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“…By understanding the effects of modulations in the doping density including effects of both the spin density as well as the doping potential, allows now calculations which probe the readout properties of the qubits, especially using techniques such as EDMR [34,35,[53][54][55]. Additionally, alternative qubits such as excited-state dopants [59] or charged dopant qubits [57,[60][61][62] can now be explored with this accurate picture of the electronic structure.…”

Section: Discussionmentioning

confidence: 99%

“…The non-spherical nature of the doping potential will be important for calculation of electron-dopant scattering cross sections. Effective mass models of doped silicon assume a spherical Coulomb potential, while some tight binding models use a spherical, Coulomb-like doping potential [28,29,56,57] and allow the surrounding atoms' electronic structure to adjust according to this potential. The anisotropic doping potentials and cell geometries calculated here could be used as alternative parameterizations for tight binding models, and they can also be used to calibrate the resulting potentials and densities calculated by tight binding models.…”

Section: A Doping Potentialmentioning

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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Electric field reduced charging energies and two-electron bound excited states of single donors in silicon

Cited by 31 publications

References 53 publications

Spatially resolving valley quantum interference of a donor in silicon

Spatially resolving valley quantum interference of a donor in silicon

Highly tunable exchange in donor qubits in silicon

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

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