Spatially resolving valley quantum interference of a donor in silicon

Abstract

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...

Interface-induced heavy-hole/light-hole splitting of acceptors in silicon

“…Recent transport spectroscopy studies of an individual acceptor embedded in nano-scale transistors have shown that for acceptors ∼10 nm away from an interface the bulk-like four-fold degeneracy is maintained [8]. Here we demonstrate that the presence of a nearby interface (<2 nm) lifts the four-fold degeneracy of the acceptorbound hole ground state by investigating the energy spectrum and wavefunctions of individual sub-surface boron acceptors using scanning tunnelling spectroscopy (STS).Recent low-temperature STM/STS studies have successfully probed the energy spectrum and wavefunctions of individual impurity atoms in Si [9][10][11] and GaAs [12,13]. These studies have revealed the influence of the semiconductor/vacuum interface on the ionization energy of sub-surface dopants [9,13], the spatially resolved structure of the dopant wavefunction [10][11][12] and the mechanisms for charge-transport through these dopants [9,11,14].…”

“…These studies have revealed the influence of the semiconductor/vacuum interface on the ionization energy of sub-surface dopants [9,13], the spatially resolved structure of the dopant wavefunction [10][11][12] and the mechanisms for charge-transport through these dopants [9,11,14]. Here, we use STS to measure the energy difference between the heavy-hole and light-hole states of individual B acceptors less than 2 nm away from the surface.…”

Highly tunable exchange in donor qubits in silicon

“…In this work, we use a large-scale atomistic tight-binding method that describes the crystal as a linear combination of atomic orbitals, and captures the full-energy spectrum of a donor in silicon, including the conduction band valley degrees of freedom, the valley-orbit interaction, 24 the Stark shift of the donor orbitals, 18 and real and momentum space images of the donor obtained by scanning tunnelling microscope experiments. 25 Using the atomistic wavefunctions, we compute the two-electron states of donor and donor clusters in the presence of an electric field from an FCI technique. The same method has been successful in solving the challenging problem of the D − state (the two-electron state of a single donor) without any fitting parameters and providing a charging energy of 45 meV (ref.…”

Spatial metrology of dopants in silicon with exact lattice site precision

“…1(b 13,14,21 , which inherently incorporates the valley-orbit (VO) interaction in order to correctly capture the atomic fine detail for both P and As cases. As the dopants are close to the surface, the effects of dimer formation (2×1 reconstruction) 12,22 and hydrogen passivation 23 are included in the tight-binding Hamiltonian (supplementary section S2).…”

“…The technique involves low temperature STM imaging 12 in conjunction with a fully quantum, large-volume treatment of the STM-dopant system. We demonstrate the metrology procedure using STM images obtained for several sub-surface P and As dopants.…”