The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modelling 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) and 1s(E) states, finding them to be 32 and 31 meV respectively. These results constitute the first ab initio confirmation of the s manifold energy levels for phosphorus donors in silicon.
Single spin qubits based on phosphorus donors in silicon are a promising candidate for a large-scale quantum computer. Despite long coherence times, achieving uniform magnetic control remains a hurdle for scale-up due to challenges in high-frequency magnetic field control at the nanometre-scale. Here, we present a proposal for a flopping-mode electric dipole spin resonance qubit based on the combined electron and nuclear spin states of a double phosphorus donor quantum dot. The key advantage of utilising a donor-based system is that we can engineer the number of donor nuclei in each quantum do…
Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling to…
Single electron transistor (SET) is an advanced tool to exploit in quantum devices. Working of such devices at room-temperature is essential for practical utilization. Dopant based single-electron devices are well studied at low-temperature although a few devices are developed for high-temperature operation with certain limitations. Here, we propose and theoretically exhibit that nitrogen (N) donor in silicon is an important candidate for effective designing of such devices. Theoretical calculation of density-of-states using semi-empirical DFT method indicates that N-donor in silicon has deep …
Micromagnet engineering for enhanced addressability of donor-cluster arrays in silicon
Southern University of Science and Technology（南方科技大学）；International Quantum Academy（国际量子科学院）；Shenzhen Branch, Hefei National Laboratory（合肥国家实验室深圳分部）；Ministry of Education Institute of Microscale Optoelectronics Shenzhen University（深圳大学微纳光电子教育部重点实验室）
Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focussed on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH$_3$) on the germ…
Excitations of impurity complexes in semiconductors can not only provide a route to fill the terahertz gap in optical technologies, but can also connect local quantum bits to scale up solid-state quantum-computing devices. However, taking into account both the interactions among electrons/holes, and the host band structures, is challenging. Here we combine first-principles band-structure calculations with quantum-chemistry methodology to evaluate the ground and excited states of a pair of phosphorous donors in silicon within s single framework. We use a broken-symmetry Hartree-Fock approach, f…
Shallow donor wavefunctions and donor-pair exchange in silicon: Ab initio theory and floating-phase Heitler-London approach
硅中浅施主的电子和核自旋是量子计算机中量子比特的有吸引力的候选者。浅施主交换门经常被调用来执行这种提议中的两个量子比特操作。本文采用密度泛函和赝势框架下的{ \it ab initio}计算方法，结合Si导带六个带边的全Bloch态，采用Kohn-Luttinger包络函数方法研究了Si中浅施主电子的性质.硅的导带边态之间的谷间干涉导致单电子束缚态电荷分布和双电子态交换耦合的振荡行为。施体电子电荷分布的行为受到来自Bloch函数的平面波和周期部分的干扰的强烈影响。对于两个捐助者，在海特勒-伦敦（HL）的方法内计算的交换耦合的振荡是由于单独的布洛赫函数的平面波部分，这是钉扎到杂质网站。该结果的鲁棒性通过放松对供体位点的相位钉扎来评估。我们介绍了一个更一般的理论方案，浮动相HL，从以前报道的施主交换振荡行为定性和定量证实。浮相形式主义提供了一个“假设”，即如何在理论上预测与更一般的限制势（如量子点）中的电子束缚态相关的电子特性中振荡行为的发生。
Donor spin in silicon have achieved record values of coherence times and single-qubit gate fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic gates, where the most natural coupling is the exchange interaction. To aid the efficient design of scalable donor-based quantum processors, we model the two-electron wave function using a full configuration interaction method within a multi-valley effective mass theory. We exploit the high computational efficiency of our code to investigate the exchange interaction, valley population, and electron densities for…
We utilize Bardeen's tunneling theory to calculate intra- and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at sho…
Phosphorus donor spins in silicon offer a number of promising characteristics for the implementation of robust qubits. Amongst various concepts for scale-up, the shared-control concept takes advantage of 3D scanning tunnelling microscope (STM) fabrication techniques to minimise the number of control lines, allowing the donors to be placed at the pitch limit of $\geq$30 nm, enabling dipole interactions. A fundamental challenge is to exploit the faster exchange interaction, however, the donor spacings required are typically 15 nm or less, and the exchange interaction is notoriously sensitive to …
