How Valley-Orbit States in Silicon Quantum Dots Probe Quantum Well Interfaces.

The energies of valley-orbit states in silicon quantum dots are determined by an as yet poorly understood interplay between interface roughness, orbital confinement, and electron interactions. Here, we report measurements of one- and two-electron valley-orbit state energies as the dot potential is modified by changing gate voltages, and we calculate these same energies using full configuration interaction calculations. The results enable an understanding of the interplay between the physical contributions and enable a new probe of the quantum well interface.

Effect of Quantum Hall Edge Strips on Valley Splitting in Silicon Quantum Wells.

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field B and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with B and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density eB/h across quantum Hall edge strips, rather than the bulk density. Based on these results, we estimate that the valley splitting increases with density at a rate of 116 µeV/10^{11} cm^{-2}, which is consistent with theoretical predictions for near-perfect quantum well top interfaces.

Atomistic Compositional Details and Their Importance for Spin Qubits in Isotope-Purified Silicon Quantum Wells.

Understanding crystal characteristics down to the atomistic level increasingly emerges as a crucial insight for creating solid state platforms for qubits with reproducible and homogeneous properties. Here, isotope concentration depth profiles in a SiGe/28Si/SiGe heterostructure are analyzed with atom probe tomography (APT) and time-of-flight secondary-ion mass spectrometry down to their respective limits of isotope concentrations and depth resolution. Spin-echo dephasing times T 2 echo = 128 µ s $T_2^\mathbf {echo}=128 \,\umu\mathrm{s}$ and valley energy splittings EVS around 200 µ e V $200 \,\umu\mathrm{e\mathrm{V}}$ have been observed for single spin qubits in this quantum well (QW) heterostructure, pointing toward the suppression of qubit decoherence through hyperfine interaction with crystal host nuclear spins or via scattering between valley states. The concentration of nuclear spin-carrying 29Si is 50 ± 20ppm in the 28Si QW. The resolution limits of APT allow to uncover that both the SiGe/28Si and the 28Si/SiGe interfaces of the QW are shaped by epitaxial growth front segregation signatures on a few monolayer scale. A subsequent thermal treatment, representative of the thermal budget experienced by the heterostructure during qubit device processing, broadens the top SiGe/28Si QW interface by about two monolayers, while the width of the bottom 28Si/SiGe interface remains unchanged. Using a tight-binding model including SiGe alloy disorder, these experimental results suggest that the combination of the slightly thermally broadened top interface and of a minimal Ge concentration of 0.3 $0.3$ % in the QW, resulting from segregation, is instrumental for the observed large E VS = 200 µ e V $E_\mathrm{VS}=200 \,\umu\mathrm{e\mathrm{V}}$ . Minimal Ge additions <1%, which get more likely in thin QWs, will hence support high EVS without compromising coherence times. At the same time, taking thermal treatments during device processing as well as the occurrence of crystal growth characteristics into account seems important for the design of reproducible qubit properties.

SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits.

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.

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si and Ge atoms within the 3D landscape of Si/SiGe interfaces can explain the observed large spread of valley splitting from measurements on many quantum dot devices. Against the prevailing belief, we propose to boost these random alloy composition fluctuations by incorporating Ge atoms in the Si quantum well to statistically enhance valley splitting.