This review describes recent groundbreaking results in Si, Si/SiGe and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade and single-shot read-out of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress towards the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics.

The ability to control matter at the atomic scale and build devices with atomic precision is central to nanotechnology. The scanning tunnelling microscope can manipulate individual atoms and molecules on surfaces, but the manipulation of silicon to make atomic-scale logic circuits has been hampered by the covalent nature of its bonds. Resist-based strategies have allowed the formation of atomic-scale structures on silicon surfaces, but the fabrication of working devices-such as transistors with extremely short gate lengths, spin-based quantum computers and solitary dopant optoelectronic devices-requires the ability to position individual atoms in a silicon crystal with atomic precision. Here, we use a combination of scanning tunnelling microscopy and hydrogen-resist lithography to demonstrate a single-atom transistor in which an individual phosphorus dopant atom has been deterministically placed within an epitaxial silicon device architecture with a spatial accuracy of one lattice site. The transistor operates at liquid helium temperatures, and millikelvin electron transport measurements confirm the presence of discrete quantum levels in the energy spectrum of the phosphorus atom. We find a charging energy that is close to the bulk value, previously only observed by optical spectroscopy.

Non-equilibrium Green function theory is formulated to meet the three main challenges of high bias quantum device modeling: self-consistent charging, incoherent and inelastic scattering, and band structure. The theory is written in a general localized orbital basis using the example of the zinc blende lattice. A Dyson equation treatment of the open system boundaries results in a tunneling formula with a generalized Fisher-Lee form for the transmission coefficient that treats injection from emitter continuum states and emitter quasi-bound states on an equal footing. Scattering is then included. Self-energies which include the effects of polar optical phonons, acoustic phonons, alloy fluctuations, interface roughness, and ionized dopants are derived. Interface roughness is modeled as a layer of alloy in which the cations of a given type cluster into islands. Two different treatments of scattering; self-consistent Born and multiple sequential scattering are formulated, described, and analyzed for numerical tractability. The relationship between the self-consistent Born and multiple sequential scattering algorithms is described, and the convergence properties of the multiple sequential scattering algorithm are numerically demonstrated by comparing with self-consistent Born calculations.

Although silicon is a promising material for quantum computation, the degeneracy of the conduction band minima (valleys) must be lifted with a splitting sufficient to ensure the formation of well-defined and long-lived spin qubits. Here we demonstrate that valley separation can be accurately tuned via electrostatic gate control in a metal-oxidesemiconductor quantum dot, providing splittings spanning 0.3-0.8 meV. The splitting varies linearly with applied electric field, with a ratio in agreement with atomistic tight-binding predictions. We demonstrate single-shot spin read-out and measure the spin relaxation for different valley configurations and dot occupancies, finding one-electron lifetimes exceeding 2 s. Spin relaxation occurs via phonon emission due to spin-orbit coupling between the valley states, a process not previously anticipated for silicon quantum dots. An analytical theory describes the magnetic field dependence of the relaxation rate, including the presence of a dramatic rate enhancement (or hot-spot) when Zeeman and valley splittings coincide.

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