J. Salfi

Spatially resolving valley quantum interference of a donor in silicon

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 have only probed wavefunctions indirectly, 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 tunnelling 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 greater than 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 for emerging schemes proposing to encode information directly in valley polarization.

Transport through a single donor in p-type silicon

Single phosphorus donors in silicon are promising candidates as qubits in the solid state. Here, we present low temperature scanning probe microscopy and spectroscopy measurements of individual phosphorus dopants deliberately placed in p-type silicon ∼1u2009nm below the surface. The ability to image individual dopants combined with scanning tunnelling spectroscopy allows us to directly study the transport mechanism through the donor. We show that for a single P donor, transport is dominated by a minority carrier recombination process with the surrounding p-type matrix. The understanding gained will underpin future studies of atomically precise mapping of donor-donor interactions in silicon.

Interplay between quantum confinement and dielectric mismatch for ultrashallow dopants

Understanding the electronic properties of dopants near an interface is a critical challenge for nanoscale devices. We have determined the effect of dielectric mismatch and quantum confinement on the ionization energy of individual acceptors beneath a hydrogen passivated silicon (100) surface. While dielectric mismatch between the vacuum and the silicon at the interface results in an image charge which enhances the binding energy of subsurface acceptors, quantum confinement is shown to reduce the binding energy. Using scanning tunneling spectroscopy we measure resonant transport through the localized states of individual acceptors. Thermal broadening of the conductance peaks provides a direct measure for the absolute energy scale. Our data unambiguously demonstrates that these two independent effects compete with the result that the ionization energy is less than 5 meV lower than the bulk value for acceptors less than a Bohr radius from the interface.

Spatially resolved resonant tunneling on single atoms in silicon

The ability to control single dopants in solid-state devices has opened the way towards reliable quantum computation schemes. In this perspective it is essential to understand the impact of interfaces and electric fields, inherent to address coherent electronic manipulation, on the dopants atomic scale properties. This requires both fine energetic and spatial resolution of the energy spectrum and wave-function, respectively. Here we present an experiment fulfilling both conditions: we perform transport on single donors in silicon close to a vacuum interface using a scanning tunneling microscope (STM) in the single electron tunneling regime. The spatial degrees of freedom of the STM tip provide a versatility allowing a unique understanding of electrostatics. We obtain the absolute energy scale from the thermal broadening of the resonant peaks, allowing us to deduce the charging energies of the donors. Finally we use a rate equations model to derive the current in presence of an excited state, highlighting the benefits of the highly tunable vacuum tunnel rates which should be exploited in further experiments. This work provides a general framework to investigate dopant-based systems at the atomic scale.

Donor wave functions in Si gauged by STM images

The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wave functions will withstand an experimental test. Such wave functions 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 resembles a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the nonmonotonic features of the current profile are consistent with the charge density fluctuations observed between successive

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

{001}

Local Kondo temperatures in atomic chains

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 wave vector to

A single-atom spin-orbit qubit in Si(Conference Presentation)

{k}_{0}=(0.82ifmmodepmelsetextpmfi{}0.03)(2ensuremath{pi}/{a}_{mathrm{Si}})

Valley Filtering in Spatial Maps of Coupling between Silicon Donors and Quantum Dots

. Unlike prior measurements, averaged over a sizable 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

Two-electron states of a group-V donor in silicon from atomistic full configuration interactions

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