Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon

Conductivity and size quantization effects in semiconductor [Formula: see text]-layer systems

We present an open-system quantum-mechanical 3D real-space study of the conduction band structure and conductive properties of two semiconductor systems, interesting for their beyond-Moore and quantum computing applications: phosphorus [Formula: see text]-layers and P [Formula: see text]-layer tunnel junctions in silicon. In order to evaluate size quantization effects on the conductivity, we consider two principal cases: nanoscale finite-width structures, used in transistors, and infinitely-wide structures, electrical properties of which are typically known experimentally. For devices widths [Formula: see text] nm, quantization effects are strong and it is shown that the number of propagating modes determines not only the conductivity, but the distinctive spatial distribution of the current-carrying electron states. For [Formula: see text] nm, the quantization effects practically vanish and the conductivity tends to the infinitely-wide device values. For tunnel junctions, two distinct conductivity regimes are predicted due to the strong conduction band quantization.

Monolayer Mo2C as anodes for magnesium-ion batteries

The adsorption and diffusion behaviors of magnesium (Mg) on monolayer Mo₂C have been investigated by the first principles method based on density functional theory (DFT). The structural stability and theoretical capacity of monolayer Mo₂C as anodes for magnesium-ion batteries (MIBs) have also been investigated. The results show that Mg prefer to occupy the H and T_C sites with the adsorption energies of - 1.439 and - 1.430, respectively, followed by B and T_Mo sites on Mo₂C monolayer. The Mg prefers to diffuse along the H-T_C-H path, furthermore, the other two possible paths (along H-B-H and H-T_Mo-H) also possess quite low energy barrier with the value of about 0.039 eV. The present results demonstrate that the adsorption energy per Mg atom and the volume expansion change mildly. The volume expansions change slightly from 0.7 to 7.08% with the variety of x, ranging from 0.167 to 2.0. The theoretical gravimetric capacity reaches to 469.791 mAhg^-1 with relatively small deformation and expansion as x = 2.0. The results mentioned above suggest that Mo₂C monolayer is one of the promising candidates for anode material of MIBs.

Ab initio calculation of energy levels for phosphorus donors in silicon

The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modeling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T ₂) and 1s(E) states, finding them to be 32 and 31 meV respectively.

A surface code quantum computer in silicon

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

Determining the electronic confinement of a subsurface metallic state

Dopant profiles in semiconductors are important for understanding nanoscale electronics. Highly conductive and extremely confined phosphorus doping profiles in silicon, known as Si:P δ-layers, are of particular interest for quantum computer applications, yet a quantitative measure of their electronic profile has been lacking. Using resonantly enhanced photoemission spectroscopy, we reveal the real-space breadth of the Si:P δ-layer occupied states and gain a rare view into the nature of the confined orbitals. We find that the occupied valley-split states of the δ-layer, the so-called 1Γ and 2Γ, are exceptionally confined with an electronic profile of a mere 0.40 to 0.52 nm at full width at half-maximum, a result that is in excellent agreement with density functional theory calculations. Furthermore, the bulk-like Si 3pz orbital from which the occupied states are derived is sufficiently confined to lose most of its pz-like character, explaining the strikingly large valley splitting observed for the 1Γ and 2Γ states.

Hybrid spin and valley quantum computing with singlet-triplet qubits

The valley degree of freedom in the electronic band structure of silicon, graphene, and other materials is often considered to be an obstacle for quantum computing (QC) based on electron spins in quantum dots. Here we show that control over the valley state opens new possibilities for quantum information processing. Combining qubits encoded in the singlet-triplet subspace of spin and valley states allows for universal QC using a universal two-qubit gate directly provided by the exchange interaction. We show how spin and valley qubits can be separated in order to allow for single-qubit rotations.

Ab initio electronic properties of dual phosphorus monolayers in silicon

IN THE MIDST OF THE EPITAXIAL CIRCUITRY REVOLUTION IN SILICON TECHNOLOGY, WE LOOK AHEAD TO THE NEXT PARADIGM SHIFT: effective use of the third dimension - in particular, its combination with epitaxial technology. We perform ab initio calculations of atomically thin epitaxial bilayers in silicon, investigating the fundamental electronic properties of monolayer pairs. Quantitative band splittings and the electronic density are presented, along with effects of the layers' relative alignment and comments on disordered systems, and for the first time, the effective electronic widths of such device components are calculated.

Valley splitting in a silicon quantum device platform

By suppressing an undesirable surface Umklapp process, it is possible to resolve the two most occupied states (1Γ and 2Γ) in a buried two-dimensional electron gas (2DEG) in silicon. The 2DEG exists because of an atomically sharp profile of phosphorus dopants which have been formed beneath the Si(001) surface (a δ-layer). The energy separation, or valley splitting, of the two most occupied bands has critical implications for the properties of δ-layer derived devices, yet until now, has not been directly measurable. Density functional theory (DFT) allows the 2DEG band structure to be calculated, but without experimental verification the size of the valley splitting has been unclear. Using a combination of direct spectroscopic measurements and DFT we show that the measured band structure is in good qualitative agreement with calculations and reveal a valley splitting of 132 ± 5 meV. We also report the effective mass and occupation of the 2DEG states and compare the dispersions and Fermi surface with DFT.

Atomistic modeling of metallic nanowires in silicon

Scanning tunneling microscope (STM) lithography has recently demonstrated the ultimate in device scaling with buried, conducting nanowires just a few atoms wide and the realization of single atom transistors, where a single P atom has been placed inside a transistor architecture with atomic precision accuracy. Despite the dimensions of the critical parts of these devices being defined by a small number of P atoms, the device electronic properties are influenced by the surrounding 10(4) to 10(6) Si atoms. Such effects are hard to capture with most modeling approaches, and prior to this work no theory existed that could explore the realistic size of the complete device in which both dopant disorder and placement are important. This work presents a comprehensive study of the electronic and transport properties of ultra-thin (<10 nm wide) monolayer highly P δ-doped Si (Si:P) nanowires in a fully atomistic self-consistent tight-binding approach. This atomistic approach covering large device volumes allows for a systematic study of disorder on the physical properties of the nanowires. Excellent quantitative agreement is observed with recent resistance measurements of STM-patterned nanowires [Weber et al., Science, 2012, 335, 64], confirming the presence of metallic behavior at the scaling limit. At high doping densities the channel resistance is shown to be insensitive to the exact channel dopant placement highlighting their future use as metallic interconnects. This work presents the first theoretical study of Si:P nanowires that are realistically extended and disordered, providing a strong theoretical foundation for the design and understanding of atomic-scale electronics.

Ab Initio electronic properties of monolayer phosphorus nanowires in silicon

Epitaxial circuitry offers a revolution in silicon technology, with components that can be fabricated on atomic scales. We perform the first ab initio calculation of atomically thin epitaxial nanowires in silicon, investigating the fundamental electronic properties of wires two P atoms thick, similar to those produced this year by Weber et al. For the first time, we catch a glimpse of disorder-related effects in the wires--a prerequisite for understanding real fabricated systems. Interwire interactions are made negligible by including 40 ML of silicon in the vertical direction (and the equivalent horizontally). Accurate pictures of band splittings and the electronic density are presented, and for the first time the effective masses of electrons in such device components are calculated.