SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits

Abstract

Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the “Wiggle Well”, whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 μeV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices.

Atomic fluctuations lifting the energy degeneracy in Si/SiGe quantum dots

“…Early calculations from scattering theories 46 suggest that the added scattering from random alloy disorder will not be the limiting factor for mobility in current 28 Si/SiGe heterostructures. However, an approximate two-fold reduction in electron mobility was recently reported when an oscillating Ge concentration of about 5% on average is incorporated in the Si quantum well 45 . We speculate that fine-tuning of the Ge concentration in the quantum well will be required for enhancing the average valley splitting while not compromising the low-disorder potential environment, which is important for scaling to large qubit systems.…”

“…This would represent a significant improvement in qubit yield for Si quantum dots. A recent report of SiGe quantum wells with oscillating Ge concentrations provides the first experimental evidence that intentionally placing Ge in the quantum well leads to significant variability and some of the highest recorded values of valley splitting 45 .…”

Practical Strategies for Enhancing the Valley Splitting in Si/SiGe Quantum Wells

“…Here, ∆ 0 is determined by the smooth quantum well confinement potential, while δ∆ describes the local Ge fluctuations caused by alloy disorder. Since E v = 2|∆|, large variations in δ∆ lead to large variations in E v , which has been verified experimentally with quantum dots [19,42].…”

“…Expanding on ideas first presented in Refs. [19] and [42], we demonstrate a universal dependence of the valley splitting on the strength of the quantum well confinement potential at the special reciprocal-space wavevector 2k 0 (we refer to this as '2k 0 theory'), corresponding to the distance between the two z valleys in the first Brillouin zone. We go on to show that deterministic and randomalloy effects can both contribute to this 2k 0 wavevector.…”

“…1(b)-1(d)], by adding Ge to the interior or the boundary of the quantum well. These include sharp interfaces [18], Ge-rich barrier layers [14], other, more complicated, superlattice barrier structures [43,44], singleatom spikes of Ge inside the quantum well [45], narrow quantum wells [18,20,29], and oscillating Ge concentrations with specially chosen oscillation wavelengths (i.e., the 'Wiggle Well' [42,46]). In this work, we examine a subset of such designs, considering both deterministic and random-alloy effects.…”